Exploring Electron–Neutrino–Argon Interactions (Springer Theses) 9783031195716, 9783031195723, 303119571X

Table of contents :
Supervisor’s Foreword
Abstract
Acknowledgements
Contents
1 Outline
References
2 Overview of Neutrino Properties
2.1 The Weak Interaction
2.2 Discovery of the Neutrino
2.3 Neutrino Oscillations
2.3.1 Neutrino Mixing
2.3.2 Neutrino Oscillations in Vacuum
2.4 Neutrino Oscillation Parameter Overview
2.4.1 Atmospheric Mixing Parameters
2.4.2 Solar Mixing Parameters
2.4.3 Reactor Mixing Parameters
2.4.4 Summary of Neutrino Oscillation Parameters
2.4.5 Short-Baseline Oscillations
2.4.6 Oscillations with Electron Neutrinos
References
3 Neutrino Interactions
3.1 Importance of Neutrino Cross Sections in Oscillation Experiments
3.2 Neutrino Interactions
3.2.1 Neutrino Generators
3.2.2 Quasi-Elastic Scattering
3.2.3 Resonant Scattering and Pion Production
3.2.4 Deep Inelastic Scattering
3.3 Nuclear Effects
3.3.1 Neutrino-Nucleus Interactions
3.3.2 Nucleon-Nucleon Correlations
3.3.3 Final State Interactions
3.4 Inclusive and Exclusive Measurements
3.5 Electron Neutrino Cross Section Measurements
3.5.1 Gargamelle
3.5.2 T2K
3.5.3 MINERvA
3.5.4 ArgoNeuT
3.5.5 Summary of Electron Neutrino Measurements
References
4 MicroBooNE as a LArTPC Detector
4.1 Liquid Argon Time Projection Chambers
4.2 Particle Interactions with Argon
4.2.1 Charged Particle Energy Loss
4.2.2 Chargeless Particle Interactions
4.2.3 Electromagnetic Showers
4.3 LArTPC Detector Effects
4.3.1 Diffusion
4.3.2 Space Charge Effect
4.3.3 Electron-Ion Recombination
4.3.4 Argon Purity
4.4 LArTPC Scintillation Light
4.4.1 Scintillation Light Production
4.4.2 Scattering and Attenuation
4.5 MicroBooNE TPC
4.5.1 MicroBooNE Charge Collection
4.5.2 MicroBooNE Light Collection System
4.6 MicroBooNE Readout and Trigger System
4.6.1 MicroBooNE Readout
4.6.2 Beam Hardware Trigger
4.6.3 Software Trigger
4.6.4 External and Unbiased Trigger
4.7 MicroBooNE Event Display
References
5 The NuMI Beam and Neutrino Flux Prediction at MicroBooNE
5.1 Neutrino Production
5.2 The NuMI Beam
5.2.1 Neutrino and Antineutrino Modes
5.2.2 NuMI Protons: Timing, Slip-Stacking and Intensity
5.3 The NuMI Beam Simulation
5.3.1 g4numi_flugg
5.3.2 g4numi
5.3.3 Beam Simulation Output
5.4 Flux Constraints with PPFX
5.5 Neutrino Flux Calculation
5.6 NuMI Flux at MicroBooNE
5.6.1 Central Value Flux Prediction
5.6.2 Flux Prediction by Neutrino Parent
5.6.3 Flux Prediction in Energy and Angle
5.7 Flux Uncertainties
5.7.1 Hadron Production Uncertainties
5.7.2 Beamline Geometry Uncertainties
5.8 Flux and Event Rate Comparisons
5.8.1 Flux Comparisons
5.8.2 Rate Comparisons
References
6 Simulation and Reconstruction in MicroBooNE
6.1 Neutrino Generation
6.2 Cosmic Modelling
6.2.1 Cosmic Simulation
6.2.2 Cosmic Overlay
6.3 Particle, Charge and Light Propagation
6.4 Detector Simulation
6.5 TPC Signal Processing
6.5.1 Deconvolution
6.5.2 ROI Finding
6.5.3 Hit Finding
6.6 Optical Reconstruction
6.6.1 Optical Hits
6.6.2 Flash Reconstruction
6.7 Pandora Reconstruction
6.8 Charge Calibration and Energy Reconstruction
6.8.1 dQ/dx Calibration
6.8.2 dE/dx Calibration and Energy Reconstruction
6.9 Reconstructed-Truth Matching
6.10 MCC8 and MCC9 Productions
6.11 Samples
6.11.1 Beam-On Sample
6.11.2 Beam-Off Sample
6.11.3 Standard Monte Carlo Sample
6.11.4 Intrinsic Electron Neutrino Monte Carlo Sample
6.11.5 Out-of-Cryostat Monte Carlo Sample
6.11.6 Normalisation Factors
6.12 MicroBooNE Coordinate System
6.13 Efficiency and Purity
References
7 Measurement of the Total Electron Neutrino and Antineutrino Cross Section on Argon
7.1 Charged Current Inclusive Selection
7.1.1 Pre-selection
7.1.2 Flash Matching
7.1.3 Vertex Reconstruction Quality
7.1.4 Shower Hit Threshold
7.1.5 Electron-Like Showers
7.1.6 Final Selection
7.1.7 Selection Performance
7.2 Total Cross Section
7.2.1 Cross Section Formula
7.2.2 Integrated Flux
7.2.3 Number of Target Nucleons
7.3 Systematic Uncertainties
7.3.1 Flux Uncertainties
7.3.2 Interaction Uncertainties
7.3.3 Detector Uncertainties
7.3.4 Out-of-Cryostat Uncertainties
7.3.5 Cosmic Simulation Uncertainty
7.3.6 POT Counting Uncertainty
7.3.7 Uncertainty on the Number of Targets
7.3.8 Systematic Uncertainty Summary
7.4 Total Cross Section Result
References
8 Selection for the CC Inclusive Differential Cross Section Measurement
8.1 Central Value and Validation
8.1.1 GENIE and PPFX Tunes
8.1.2 Out-of-Cryostat Interactions Correction
8.1.3 Flash Timing Distribution
8.2 Electron Neutrino and Antineutrino Selection
8.2.1 Event Classifications
8.2.2 Distributions Before Selection
8.2.3 Selection Overview
8.2.4 Neutrino Identification
8.2.5 Containment
8.2.6 Cosmic Rejection
8.2.7 Shower Identification
8.2.8 Electron-Photon Separation
8.3 Post Selection: Study of Kinematic Variables
8.3.1 Angular Distributions
8.3.2 Shower and Track Multiplicity
8.3.3 Reconstructed Shower Energy and Angle Performance
References
9 Uncertainties and Principles of Extracting the Differential Cross Section
9.1 Cross Section Methodology
9.1.1 Flux-Averaged Differential Cross Section Formula
9.1.2 Detector Response and Flux-Normalised Event Rate
9.1.3 Forward Folding
9.1.4 Unfolding
9.1.5 Integrated Flux
9.1.6 Number of Target Nucleons
9.2 Systematic Uncertainties
9.2.1 Flux Systematic Uncertainty
9.2.2 Interaction Model Systematic Uncertainties
9.2.3 Detector Uncertainties
9.2.4 Data Statistical Uncertainties
9.2.5 MC Statistics for the Response Matrix
9.2.6 Uncertainties from POT Counting, Out-of-Cryostat Simulation and Number of Targets
9.2.7 Beam-Off Normalisation
9.2.8 Summary of Systematic Uncertainty
9.2.9 Summary of Total Uncertainty
References
10 The First CC Inclusive Differential Electron Neutrino and Antineutrino Cross Section on Argon in MicroBooNE
10.1 Total Cross Section Result
10.2 Forward Folded Result
10.3 Wiener-SVD Unfolded Result
10.4 Generator Comparisons
10.4.1 Total Cross Section Generator Comparison
10.4.2 Forward and Unfolded Cross Section Generator Comparisons
10.4.3 Comparison with the MCC8 Result
References
11 Conclusion and Outlook
References
Appendix A Additional Event Rate Distributions
Appendix B Differential Cross Section Bin Optimisations
Appendix C Resolution, Purity and Completeness for the Differential Cross Section Variables
C.1 Shower Purity
C.2 Shower Completeness
C.3 Shower Resolutions
Appendix D Cross Section Validation
D.1 Fake Data Test 1
D.1.1 Fake Data Test 1: Total Cross Section
D.1.2 Fake Data Test 1: Differential Cross Section
D.2 Fake Data Test 2: Data Extracted Cross Section
D.3 Model Independent Response Matrix
Appendix E Event Displays

Citation preview

Springer Theses Recognizing Outstanding Ph.D. Research

Krishan V. J. Mistry

Exploring Electron-Neutrino– Argon Interactions

Springer Theses Recognizing Outstanding Ph.D. Research

Aims and Scope The series “Springer Theses” brings together a selection of the very best Ph.D. theses from around the world and across the physical sciences. Nominated and endorsed by two recognized specialists, each published volume has been selected for its scientific excellence and the high impact of its contents for the pertinent field of research. For greater accessibility to non-specialists, the published versions include an extended introduction, as well as a foreword by the student’s supervisor explaining the special relevance of the work for the field. As a whole, the series will provide a valuable resource both for newcomers to the research fields described, and for other scientists seeking detailed background information on special questions. Finally, it provides an accredited documentation of the valuable contributions made by today’s younger generation of scientists.

Theses may be nominated for publication in this series by heads of department at internationally leading universities or institutes and should fulfill all of the following criteria • They must be written in good English. • The topic should fall within the confines of Chemistry, Physics, Earth Sciences, Engineering and related interdisciplinary fields such as Materials, Nanoscience, Chemical Engineering, Complex Systems and Biophysics. • The work reported in the thesis must represent a significant scientific advance. • If the thesis includes previously published material, permission to reproduce this must be gained from the respective copyright holder (a maximum 30% of the thesis should be a verbatim reproduction from the author’s previous publications). • They must have been examined and passed during the 12 months prior to nomination. • Each thesis should include a foreword by the supervisor outlining the significance of its content. • The theses should have a clearly defined structure including an introduction accessible to new PhD students and scientists not expert in the relevant field. Indexed by zbMATH.

Krishan V. J. Mistry

Exploring Electron-Neutrino–Argon Interactions Doctoral Thesis accepted by The University of Manchester, Manchester, United Kingdom

Author Dr. Krishan V. J. Mistry The University of Texas at Arlington Arlington, USA

Supervisor Dr. Andrzej Szelc The University of Edinburgh Edinburgh, UK

ISSN 2190-5053 ISSN 2190-5061 (electronic) Springer Theses ISBN 978-3-031-19571-6 ISBN 978-3-031-19572-3 (eBook) https://doi.org/10.1007/978-3-031-19572-3 © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 This work is subject to copyright. All rights are solely and exclusively licensed by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors, and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, expressed or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. This Springer imprint is published by the registered company Springer Nature Switzerland AG The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland

Supervisor’s Foreword

Neutrinos are one of the most puzzling particles known to physicists. There are billions of them crossing our bodies every second, yet they interact so weakly that barely a single one might interact throughout our lifetime. Ever since their discovery, neutrinos have often behaved in an unexpected way challenging our understanding of particle physics and pushing physicists to expand our models and learn more about the universe around us. One of the first such occurrences was the Ray Davis experiment at the Homestake mine in South Dakota. This experiment for 30 years measured the flux of electron-neutrinos produced in our Sun by counting radioactive argon atoms the neutrinos created when interacting with chlorine atoms found in a cleaning fluid filling the detector. The obtained results, which always showed a deficit of the neutrinos compared to our expectations from the Sun, ended up being the first proof that neutrinos can change flavour via a process called oscillation. This in turn meant that neutrinos have a non-zero mass, which was contrary to previous expectations and led to a necessary updating of our understanding of particle physics and a whole new field of experimental physics focussed on measuring how neutrinos oscillate. In the last two decades, our measurements of neutrino oscillations have become more and more precise, particularly thanks to the availability of man-made sources of neutrinos such as accelerator beams. Controlling and knowing the flux and energy of neutrinos emitted by magnetically focussed mesons such as pions and kaons produced in an accelerator complex enables measurements at long and short baselines with a precision that is very difficult to obtain with neutrinos from naturally existing sources. Accelerators produce beams that are almost exclusively made of a different flavour—the muon neutrinos. However, some electron-neutrinos can be found in such beams and, as it turns out, they may hold the key to answering several of the big open questions in neutrino physics. Several neutrino experiments have in the last two decades observed unexpected excesses of electron-neutrinos in muon-neutrino beams which, if interpreted as oscillations on very short distances, could imply the existence of a completely new particle—the sterile neutrino. In parallel, muon neutrinos oscillating into electron-neutrinos at distances on the orders of a thousand kilometres can tell us what is the so-called neutrino mass ordering, i.e. whether v

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Supervisor’s Foreword

the electron-neutrino is the lightest or the heaviest of the three known flavours and whether the so-called charge-parity (CP) symmetry is broken in neutrino oscillations. The latter is a fundamental measurement: if a CP asymmetry were to be observed it could lead us to finally explaining why our Universe is predominantly built out of matter and not equal parts of matter and anti-matter! To resolve these pressing experimental questions, excellent particle detectors are needed. The neutrino community has largely chosen liquid argon time projection chambers (LArTPC) as the detectors for the job. The LArTPCs forming the Short Baseline Neutrino Programme at Fermilab, near Chicago, called SBND, MicroBooNE and ICARUS will search for electron-neutrinos appearing on short distances to determine the existence of the sterile neutrino. Meanwhile, an international collaboration of over a thousand physicists is building the multi-kTon Deep Underground Neutrino Experiment (DUNE) to search for electron-neutrinos appearing over a distance of 1300 km in a beam sent from Fermilab to South Dakota. DUNE will be built in the Sanford Underground Research Facility (SURF) which happens to be located in the same mine where the Davis experiment was built. So, in a strange way of history repeating, electron-neutrinos and argon will return to the same place to again be at the centre of a major physics riddle. For these measurements to succeed, it is crucial to precisely understand how neutrinos, and specifically electron-neutrinos, interact with an argon nucleus. Argon is a relatively large and complex nucleus and nuclear effects can play a significant role in the interactions often making it harder to understand what happened in a given interaction. The resulting uncertainties can be reduced by dedicated measurements that help us model how neutrino–argon interactions work in practice. However, until 2020, no measurements of electron-neutrino interactions on argon existed. This is where Krishan Mistry’s thesis titled, “Exploring Electron Neutrino-Argon Interactions” comes in. It presents two of the first three measurements of the electronneutrino cross section on argon ever made, both using the largest sample of electronneutrinos in an argon detector by an order of magnitude. These measurements were the first demonstration of large-scale automated reconstruction of electron-neutrino events in a LArTPC, demonstrating the electron-photon separation within this framework. The measurements were enabled by employing the second neutrino beam at Fermilab—the NuMI beam. The thesis describes the first implementation of this highly off-axis at MicroBooNE beam, which has a high electron-neutrino component, for a neutrino measurement in MicroBooNE. This work has begun a whole new set of analyses being developed by the MicroBooNE collaboration focussing on measurements of cross sections as well as searches beyond the standard model physics. The key takeaway is that the result from the thesis presented here paves the way for the “golden channel” measurements of electron-neutrinos appearing in the search for CP violation, the neutrino mass-ordering as well as for the fourth, sterile, family of neutrinos. The research presented in this thesis has been published in two

Supervisor’s Foreword

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articles in Phys. Rev. D, and is being used as a reference for future analyses working on neutrino cross sections. Edinburgh, UK August 2022

Dr. Andrzej Szelc

Abstract

The MicroBooNE experiment uses a liquid argon time projection chamber (LArTPC) located at Fermilab, Chicago. MicroBooNE is able to detect neutrinos from two accelerators: on-axis from the Booster Neutrino Beam (BNB) and off-axis from the Neutrinos at the Main Injector (NuMI). While one of the primary objectives of the MicroBooNE experiment is to search for short-baseline neutrino oscillations using the BNB, it also has a rich program of R&D, neutrino-argon cross section measurements and beyond the standard model searches. This thesis presents a detailed study of the off-axis neutrino flux from the NuMI beam at MicroBooNE as well as measurements of the charged current flux-averaged total and differential electron-neutrino and antineutrino cross section on argon using this beam. The data used in these measurements was taken during the first year of MicroBooNE running while the NuMI beam was in forward horn current mode. These are the first high statistics measurements of electron-neutrino–argon interactions and include the first measurement of this cross section as a function of the outgoing electron energy and with full angular coverage. The measurement is compared to the GENIE and NuWro generators and shows consistency with both.

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Acknowledgements

The journey of completing a Ph.D. over the last 3.5 years has been an amazing experience. I have met some great people along the way who are extremely intelligent and have been a pleasure to work with. Having the opportunity to study neutrinos and uncover the properties of this particle has been very special and is something I have a great enjoyment doing every single day. I very much have to thank my supervisor Andrzej for giving me this experience and the countless hours of his time he has given to help me improve as a scientist. I couldn’t have had a better supervisor and I don’t know where I would be if I never did that Master’s project with you. I am extremely grateful for the help, experience and amazing advice you have given to me. Thank you so much! A special thank you to Elena who has been very supportive for me and helped me massively to develop as a scientist. I am thankful for your leadership, friendship and advice you have given me. Owen and Patrick, thanks for being able to put up with living with me in Fermilab, you guys honestly were great company and a pleasure to share an apartment with despite the never-ending pain with Windscape. Marina and Nicola, thanks for helping me get through this Ph.D. and it was great to discuss electron-neutrinos every week! Davide, thanks for being such a great person to hang out with and for always being so helpful in my early days of starting my Ph.D. Vincent, thanks for the hours you had to put up with me while we got through many of those evaporations, we got there eventually! Colton, thanks for being such a great mentor and introducing me to D&D for the first time. Andy F., thanks for all the amazing advice you gave me. Pawel, thanks for helping me solve the many software problems I had. Rhiannon, Andy and Tom, thanks for all those great nights at Site 56 and our rather adventurous journey to the South! Wouter, thanks for letting me stay in Boston and for all those great times we had. Adam, thanks for your aura of calm on MicroBooNE. Marco, thanks for helping with the bombardment of cross section questions I had. Davio and Michelle I will never forget that thanksgetti (or whatever you called it) that you cooked for me. Avinay, thanks for hosting such great movie nights. Kirsty, thanks for hosting that amazing chicken painting party and providing so much invaluable advice on cross sections. Iker, thanks for introducing me to delicious-tasting Mexican food and being a great friend to hang out with. xi

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Acknowledgements

Andrew M., thanks for always cracking me up. Thanks to Lauren, Sam, Ivan, Afro, Lauren, Kathryn, Mark, Iris, Yeon-jae and Gray for all those Taco Tuesdays we got to enjoy. Donal and Martha, while we didn’t get to see each other after our LTA, I very much appreciate the many Wetherspoons and endless banter after a long-day work. Thanks to all my colleagues who I haven’t been able to fit in here from Manchester, MicroBooNE and Fermilab for making my Ph.D. such an amazing experience and for all the advice you have given to me! Finally, I would like to sincerely thank my Mum, Dad, Bro and Sis for helping me get through this, especially through a year like 2020. I couldn’t have done this without you and I am extremely grateful for everything you have done for me. I dedicate this thesis to you.

Contents

1

Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1 2

2

Overview of Neutrino Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1 The Weak Interaction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2 Discovery of the Neutrino . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3 Neutrino Oscillations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3.1 Neutrino Mixing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3.2 Neutrino Oscillations in Vacuum . . . . . . . . . . . . . . . . . . . . 2.4 Neutrino Oscillation Parameter Overview . . . . . . . . . . . . . . . . . . . . 2.4.1 Atmospheric Mixing Parameters . . . . . . . . . . . . . . . . . . . . 2.4.2 Solar Mixing Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4.3 Reactor Mixing Parameters . . . . . . . . . . . . . . . . . . . . . . . . . 2.4.4 Summary of Neutrino Oscillation Parameters . . . . . . . . . 2.4.5 Short-Baseline Oscillations . . . . . . . . . . . . . . . . . . . . . . . . . 2.4.6 Oscillations with Electron Neutrinos . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3 3 4 5 5 6 7 8 9 9 9 9 11 11

3

Neutrino Interactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1 Importance of Neutrino Cross Sections in Oscillation Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2 Neutrino Interactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.1 Neutrino Generators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.2 Quasi-Elastic Scattering . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.3 Resonant Scattering and Pion Production . . . . . . . . . . . . . 3.2.4 Deep Inelastic Scattering . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3 Nuclear Effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3.1 Neutrino-Nucleus Interactions . . . . . . . . . . . . . . . . . . . . . . 3.3.2 Nucleon-Nucleon Correlations . . . . . . . . . . . . . . . . . . . . . . 3.3.3 Final State Interactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4 Inclusive and Exclusive Measurements . . . . . . . . . . . . . . . . . . . . . . 3.5 Electron Neutrino Cross Section Measurements . . . . . . . . . . . . . . .

15 15 17 17 18 19 20 20 21 22 23 25 26 xiii

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3.5.1 Gargamelle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.5.2 T2K . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.5.3 MINERvA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.5.4 ArgoNeuT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.5.5 Summary of Electron Neutrino Measurements . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

27 27 28 29 29 30

4

MicroBooNE as a LArTPC Detector . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1 Liquid Argon Time Projection Chambers . . . . . . . . . . . . . . . . . . . . 4.2 Particle Interactions with Argon . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2.1 Charged Particle Energy Loss . . . . . . . . . . . . . . . . . . . . . . 4.2.2 Chargeless Particle Interactions . . . . . . . . . . . . . . . . . . . . . 4.2.3 Electromagnetic Showers . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3 LArTPC Detector Effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3.1 Diffusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3.2 Space Charge Effect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3.3 Electron-Ion Recombination . . . . . . . . . . . . . . . . . . . . . . . . 4.3.4 Argon Purity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.4 LArTPC Scintillation Light . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.4.1 Scintillation Light Production . . . . . . . . . . . . . . . . . . . . . . 4.4.2 Scattering and Attenuation . . . . . . . . . . . . . . . . . . . . . . . . . 4.5 MicroBooNE TPC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.5.1 MicroBooNE Charge Collection . . . . . . . . . . . . . . . . . . . . 4.5.2 MicroBooNE Light Collection System . . . . . . . . . . . . . . . 4.6 MicroBooNE Readout and Trigger System . . . . . . . . . . . . . . . . . . . 4.6.1 MicroBooNE Readout . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.6.2 Beam Hardware Trigger . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.6.3 Software Trigger . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.6.4 External and Unbiased Trigger . . . . . . . . . . . . . . . . . . . . . . 4.7 MicroBooNE Event Display . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

33 33 34 34 36 37 39 39 40 40 41 42 42 43 43 44 45 46 46 46 47 47 48 49

5

The NuMI Beam and Neutrino Flux Prediction at MicroBooNE . . . 5.1 Neutrino Production . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2 The NuMI Beam . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2.1 Neutrino and Antineutrino Modes . . . . . . . . . . . . . . . . . . . 5.2.2 NuMI Protons: Timing, Slip-Stacking and Intensity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.3 The NuMI Beam Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.3.1 g4numi_flugg . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.3.2 g4numi . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.3.3 Beam Simulation Output . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.4 Flux Constraints with PPFX . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.5 Neutrino Flux Calculation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.6 NuMI Flux at MicroBooNE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

51 51 53 54 55 56 57 57 58 58 60 63

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5.6.1 Central Value Flux Prediction . . . . . . . . . . . . . . . . . . . . . . 5.6.2 Flux Prediction by Neutrino Parent . . . . . . . . . . . . . . . . . . 5.6.3 Flux Prediction in Energy and Angle . . . . . . . . . . . . . . . . 5.7 Flux Uncertainties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.7.1 Hadron Production Uncertainties . . . . . . . . . . . . . . . . . . . . 5.7.2 Beamline Geometry Uncertainties . . . . . . . . . . . . . . . . . . . 5.8 Flux and Event Rate Comparisons . . . . . . . . . . . . . . . . . . . . . . . . . . 5.8.1 Flux Comparisons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.8.2 Rate Comparisons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

63 65 66 69 69 72 74 75 76 77

Simulation and Reconstruction in MicroBooNE . . . . . . . . . . . . . . . . . . 6.1 Neutrino Generation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2 Cosmic Modelling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2.1 Cosmic Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2.2 Cosmic Overlay . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.3 Particle, Charge and Light Propagation . . . . . . . . . . . . . . . . . . . . . . 6.4 Detector Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.5 TPC Signal Processing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.5.1 Deconvolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.5.2 ROI Finding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.5.3 Hit Finding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.6 Optical Reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.6.1 Optical Hits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.6.2 Flash Reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.7 Pandora Reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.8 Charge Calibration and Energy Reconstruction . . . . . . . . . . . . . . . 6.8.1 dQ/dx Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.8.2 dE/dx Calibration and Energy Reconstruction . . . . . . . . . 6.9 Reconstructed-Truth Matching . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.10 MCC8 and MCC9 Productions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.11 Samples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.11.1 Beam-On Sample . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.11.2 Beam-Off Sample . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.11.3 Standard Monte Carlo Sample . . . . . . . . . . . . . . . . . . . . . . 6.11.4 Intrinsic Electron Neutrino Monte Carlo Sample . . . . . . 6.11.5 Out-of-Cryostat Monte Carlo Sample . . . . . . . . . . . . . . . . 6.11.6 Normalisation Factors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.12 MicroBooNE Coordinate System . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.13 Efficiency and Purity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

79 79 80 81 81 81 82 82 83 83 83 84 84 85 85 86 86 88 89 89 90 90 90 91 91 92 92 93 95 96

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Measurement of the Total Electron Neutrino and Antineutrino Cross Section on Argon . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.1 Charged Current Inclusive Selection . . . . . . . . . . . . . . . . . . . . . . . . 7.1.1 Pre-selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.1.2 Flash Matching . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.1.3 Vertex Reconstruction Quality . . . . . . . . . . . . . . . . . . . . . . 7.1.4 Shower Hit Threshold . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.1.5 Electron-Like Showers . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.1.6 Final Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.1.7 Selection Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.2 Total Cross Section . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.2.1 Cross Section Formula . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.2.2 Integrated Flux . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.2.3 Number of Target Nucleons . . . . . . . . . . . . . . . . . . . . . . . . 7.3 Systematic Uncertainties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.3.1 Flux Uncertainties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.3.2 Interaction Uncertainties . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.3.3 Detector Uncertainties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.3.4 Out-of-Cryostat Uncertainties . . . . . . . . . . . . . . . . . . . . . . 7.3.5 Cosmic Simulation Uncertainty . . . . . . . . . . . . . . . . . . . . . 7.3.6 POT Counting Uncertainty . . . . . . . . . . . . . . . . . . . . . . . . . 7.3.7 Uncertainty on the Number of Targets . . . . . . . . . . . . . . . 7.3.8 Systematic Uncertainty Summary . . . . . . . . . . . . . . . . . . . 7.4 Total Cross Section Result . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

99 99 100 101 101 101 102 103 103 105 105 106 106 107 108 108 109 110 110 111 111 111 112 113

Selection for the CC Inclusive Differential Cross Section Measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.1 Central Value and Validation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.1.1 GENIE and PPFX Tunes . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.1.2 Out-of-Cryostat Interactions Correction . . . . . . . . . . . . . . 8.1.3 Flash Timing Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . 8.2 Electron Neutrino and Antineutrino Selection . . . . . . . . . . . . . . . . 8.2.1 Event Classifications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.2.2 Distributions Before Selection . . . . . . . . . . . . . . . . . . . . . . 8.2.3 Selection Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.2.4 Neutrino Identification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.2.5 Containment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.2.6 Cosmic Rejection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.2.7 Shower Identification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.2.8 Electron-Photon Separation . . . . . . . . . . . . . . . . . . . . . . . . 8.3 Post Selection: Study of Kinematic Variables . . . . . . . . . . . . . . . . . 8.3.1 Angular Distributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.3.2 Shower and Track Multiplicity . . . . . . . . . . . . . . . . . . . . . .

115 115 115 116 116 119 119 121 122 125 127 130 133 137 141 143 143

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8.3.3

Reconstructed Shower Energy and Angle Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148 9

Uncertainties and Principles of Extracting the Differential Cross Section . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.1 Cross Section Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.1.1 Flux-Averaged Differential Cross Section Formula . . . . 9.1.2 Detector Response and Flux-Normalised Event Rate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.1.3 Forward Folding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.1.4 Unfolding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.1.5 Integrated Flux . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.1.6 Number of Target Nucleons . . . . . . . . . . . . . . . . . . . . . . . . 9.2 Systematic Uncertainties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.2.1 Flux Systematic Uncertainty . . . . . . . . . . . . . . . . . . . . . . . . 9.2.2 Interaction Model Systematic Uncertainties . . . . . . . . . . . 9.2.3 Detector Uncertainties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.2.4 Data Statistical Uncertainties . . . . . . . . . . . . . . . . . . . . . . . 9.2.5 MC Statistics for the Response Matrix . . . . . . . . . . . . . . . 9.2.6 Uncertainties from POT Counting, Out-of-Cryostat Simulation and Number of Targets . . . . 9.2.7 Beam-Off Normalisation . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.2.8 Summary of Systematic Uncertainty . . . . . . . . . . . . . . . . . 9.2.9 Summary of Total Uncertainty . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

10 The First CC Inclusive Differential Electron Neutrino and Antineutrino Cross Section on Argon in MicroBooNE . . . . . . . . 10.1 Total Cross Section Result . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.2 Forward Folded Result . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.3 Wiener-SVD Unfolded Result . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.4 Generator Comparisons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.4.1 Total Cross Section Generator Comparison . . . . . . . . . . . 10.4.2 Forward and Unfolded Cross Section Generator Comparisons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.4.3 Comparison with the MCC8 Result . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

151 151 151 152 153 154 155 156 157 158 160 165 168 169 169 170 170 172 175 177 177 178 179 180 181 182 182 184

11 Conclusion and Outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 186 Appendix A: Additional Event Rate Distributions . . . . . . . . . . . . . . . . . . . . 187 Appendix B: Differential Cross Section Bin Optimisations . . . . . . . . . . . . 189

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Appendix C: Resolution, Purity and Completeness for the Differential Cross Section Variables . . . . . . . . . . . . . . 193 Appendix D: Cross Section Validation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197 Appendix E: Event Displays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 209

Chapter 1

Outline

The precise knowledge of the electron neutrino cross section is fundamental for tests of lepton universality, making meaningful interpretations of neutrino oscillations and beyond the Standard Model search experiments involving electron neutrinos. Moreover, the appearance of electron neutrinos in a beam of predominantly muon neutrinos is the key signature in searches for sterile neutrinos in short-baseline experiments and measurements of Charge-Parity (CP) violation in long-baseline oscillation experiments. Only a handful of electron neutrino cross section measurements in the hundred MeV to GeV range exist and only one of them on argon as the target nucleus: the result from the ArgoNeuT experiment [1]. Therefore, there is a need for new, large statistics, electron-neutrino cross section measurements which would be valuable to the Short-Baseline Neutrino (SBN) programme [2] and the Deep Underground Neutrino Experiment (DUNE) [3]. This thesis covers the development of the tools to predict the neutrino flux from the off-axis Neutrinos at the Main Injector (NuMI) beam at MicroBooNE. In addition, measurements of the charged current (CC) inclusive flux-averaged total and differential electron neutrino and antineutrino cross sections on argon are presented. The structure of the thesis is as follows: Chap. 2 describes the history and current state of neutrino physics with an emphasis on neutrino oscillations. Chapter 3 covers the physics of neutrino interactions and measurements of the electron neutrino cross section. The physics and operation of the MicroBooNE detector are discussed in Chap. 4 while Chap. 5 describes the method of calculating the off-axis NuMI neutrino flux at MicroBooNE. The validation of the flux was performed in collaboration with Katrina Miller who worked on reproducing the prediction and uncertainties at the NOvA near and MINERvA detectors. A description of the MicroBooNE simulation software and reconstruction used in this thesis is covered in Chap. 6. The measurement of the CC flux-averaged total cross section is discussed in Chap. 7. The electron neutrino and antineutrino selection for this measurement was originally developed by Colton Hill [4] with my contribution to this analysis being the © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 K. V. J. Mistry, Exploring Electron-Neutrino–Argon Interactions, Springer Theses, https://doi.org/10.1007/978-3-031-19572-3_1

1

2

1 Outline

evaluation of the systematic uncertainties and finalising the analysis for publication which has been published in the Phys. Rev. D journal [5]. The remainder of the thesis describes an analysis performed using a framework I developed and is dedicated to the measurement of the CC flux-averaged differential cross section as a function of the electron/positron energy and angle. This measurement has also been published in the Phys. Rev. D journal [6]. Chapter 8 describes the selection developed to identify electron neutrinos and antineutrinos in the MicroBooNE detector and the performance of this selection. Chapter 9 describes the method for extracting the differential cross section as well as the systematic uncertainties associated with the measurement. Finally, Chap. 10 shows the results of the differential measurement.

References 1. Acciarri R et al (2020) First measurement of electron neutrino scattering cross section on argon. Phys Rev D 102(1):011101 2. Antonello M et al (2015) A proposal for a three detector short-baseline neutrino oscillation program in the fermilab booster neutrino beam. arXiv: 1503.01520 [physics.ins-det] 3. Abi B et al (2020) Long-baseline neutrino oscillation physics potential of the DUNE experiment. Eur Phys J C 80(10):978 4. Hill C (2019) Measurement of the charged-current inclusive electron neutrino and electron antineutrino cross section using the MicroBooNE detector in the NuMI beam. Ph.D. dissertation, University of Manchester 5. Abratenko P et al (2021) Measurement of the flux-averaged inclusive charged current electron neutrino and antineutrino cross section on argon using the NuMI beam and the MicroBooNE detector. Phys Rev D 104(5):052002 6. Abratenko P et al (2022) First measurement of inclusive electron-neutrino and antineutrino charged current differential cross sections in charged lepton energy on argon in MicroBooNE. Phys Rev D 105(5):L051102

Chapter 2

Overview of Neutrino Properties

The neutrino is a chargeless, spin 1/2 lepton that interacts only through the weak interaction and gravity. The discovery that neutrinos oscillate, which also implies they have mass, has enabled one of the most powerful ways to study the properties of this particle and could help us to understand some of the most puzzling questions in the field of particle physics. For example, studying if there are differences in oscillations between neutrinos and antineutrinos could help us understand why we live in a matter dominated universe. This chapter will describe the history of neutrinos and give an overview of the model and measurements of neutrino oscillations.

2.1 The Weak Interaction Birth of the Neutrino and the Weak Interaction The idea of the neutrino was first postulated by Pauli in 1930 to rescue energy conservation in the nuclear beta-decay process by introducing a massless, neutral particle that would carry away the missing energy [1]. A few years later, Fermi coined the name of this particle as the neutrino in his theory of weak interactions. In his theory, a direct coupling between the four fermions involved in beta decay, n → p + e− + ν¯e , was introduced. The matrix element, M, which is related to the probability of the decay happening, was given by: GF M = √ [u¯ n γ μ u p ][u¯ νe γμ u e ], 2

(2.1)

where G F = 1.166 × 10−5 GeV−2 is the Fermi coupling constant, u x is the Dirac spinor of particle x and γ μ /γμ are the Dirac gamma matrices [2]. Similar to elec© The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 K. V. J. Mistry, Exploring Electron-Neutrino–Argon Interactions, Springer Theses, https://doi.org/10.1007/978-3-031-19572-3_2

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2 Overview of Neutrino Properties

tromagnetic (EM) interactions, this interaction only included a vector component. However, because it was described as point-like with no propagator, the calculated cross section for this process was proportional to the energy of the neutrino squared. As a result, the theory broke down at high energies where the amplitude of the matrix element could exceed 1 and violate unitarity [3]. Following the experiment carried out by Wu in 1956 studying the asymmetry of electrons emitted in the beta-decay of polarized 60 Co nuclei [4], it was discovered that the weak interaction maximally violated the parity symmetry. Further properties of the weak interaction were revealed by Goldhaber, Grodzins and Sunyar who were able to show that neutrinos are only produced in a left-handed helicity state (spin anti-parallel to momentum) and antineutrinos were only produced in a right-handed helicity state (spin parallel to momentum) [5]. With this result, along with Wu’s experiment, it could be deduced that for all ultra-relativistic fermions, the weak interaction only couples to left-handed fermions and right-handed antifermions [6]. With these discoveries, the vector-only component of Fermi’s theory was not enough to describe the parity-violating property of the weak interaction. To solve this, the V-A (vector minus axial) theory developed by Sudarshan and Marshak [7], and independently by Feynman and Gell-Mann [8], introduced an axial-vector (A) component in addition to the vector component (V). Parity violation could then be introduced via the interference between the vector and axial components [6] and the matrix element for beta decay could be now written as, GF M = √ [u¯ n γ u (1 − γ 5 )u p ][u¯ νe γu (1 − γ 5 )u e ], 2

(2.2)

where the terms γ μ /γμ and γ μ γ 5 /γμ γ 5 correspond to the vector and axial parts respectively. While the introduction of the V-A theory was able to describe the parity-violating nature of weak interactions, there was still the issue of its behaviour at high energy. This was solved with the introduction of the exchange bosons in the weak interaction, W ± and Z 0 . The range of the weak force is then proportional to the inverse of the squared mass of the weak boson resulting in its very short range.

2.2 Discovery of the Neutrino Discovery of the Neutrino The neutrino is notoriously difficult to detect because it is the only particle in the Standard Model to interact solely through the weak interaction. As a result, it took more than 20 years after it was first postulated before the observation of the electron antineutrino by Reines and Cowan in 1956. To discover the neutrino, they utilised the large flux of antineutrinos from the Savannah River nuclear reactor [9]. They built a detector consisting of layers of scintillator and cadmium-doped water which is sensitive to the inverse beta-decay reaction,

2.3 Neutrino Oscillations

5

ν¯e + p → e+ + n.

(2.3)

The signature of this interaction is a prompt scintillation light signal coming from the annihilation of the positron and a ∼10 µs delayed scintillation signal produced from neutron capture on 144 Cd. They compared the measured rate of this process while the reactor was on compared to when it was off and found clear evidence of electron antineutrinos originating from the reactor. Two Neutrino Flavours Lederman, Schwartz and Steinberger were able to demonstrate there were two flavours of neutrino after they discovered the muon neutrino in 1962 [10]. They created a beam of neutrinos from accelerating protons to 15 GeV and colliding them with a Beryllium target. This collision produced an unfocussed beam rich in pions whose primary decay mode is to muon neutrinos via π ± → μ± + νμ (ν¯μ ). They identified 34 single-muon candidates (E >300 MeV) originating from inside their sparkchamber detector compared to 8 electron-like candidates. The creation of muons from neutrino interactions inside their detector compared to electrons demonstrated that muon neutrinos are distinct particles from electron neutrinos. Discovery of the Tau Neutrino Tau neutrinos are much more difficult to detect due to the high energy needed to produce a tau lepton which has a rest mass of 1.8 GeV. The DONUT experiment achieved the first detection of the tau neutrinos in 2001 by leveraging the high proton energies from the Tevatron [11]. Similar to the method of neutrino production from Lederman, Schwartz and Steinberger, protons were accelerated up to 800 GeV and were collided with a tungsten target. In these collisions, the higher energy of the proton beam enabled Ds mesons to be produced, which have a sizeable branching fraction (6%) to tau neutrinos. The DONUT collaboration was able to identify four tau neutrinos by searching for the appearance of tau leptons using an emulsion-type detector

2.3 Neutrino Oscillations This section will give a brief overview of the formulism of neutrino oscillations. For a detailed description, see Refs. [12–14] for a modern review.

2.3.1 Neutrino Mixing The concept of neutrino oscillations was first suggested by Pontecorvo. By drawing similarities with neutral kaon mixing K 0  K¯ 0 , he suggested there could be mixing between neutrinos and antineutrinos in 1957 [15]. At the time of this suggestion, only the electron neutrino had been discovered, but with the subsequent discovery of the

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2 Overview of Neutrino Properties

muon neutrino, Pontecorvo expanded this idea to oscillation between two flavours in 1967 [16], although it should be noted that the idea of two neutrino oscillations was suggested earlier by Maki, Nakagawa and Sakata in 1962 [17]. The initial theory of two-neutrino oscillations can be expanded to three flavours.1 Using the notation outlined in Ref. [14], the weak (flavour) eigenstates, να , are constructed via a coherent combination of mass eigenstates,2 νi , |να  =

n 

∗ Uαi |νi ,

(2.4)

i=1

where Uα j are the elements of the Pontecorvo-Maki-Nakagawa-Sakata (PMNS) 3 × 3 mixing matrix, ⎛

Uα j

⎞ Ue1 Ue2 Ue3 = ⎝Uμ1 Uμ2 Uμ3 ⎠ . Uτ 1 Uτ 2 Uτ 3

(2.5)

The PMNS matrix is a unitary matrix that satisfies the relations UU † = U † U = 1. It is described by 9 parameters in total consisting of 3 mixing angles and 6 phases. Without changing the physics, some of these phases are removed because of the freedom to change the phase of the charged lepton and neutrino fields: |lα  → eiφα |lα  and |νi  → eiφi |νi . Since there are 5 independent phases, 5 phases from the PMNS matrix can be removed leaving three mixing angles, θ12 , θ13 , θ23 and a Charge-Parity (CP) violating phase, δCP .

2.3.2 Neutrino Oscillations in Vacuum For a neutrino that is created from a weak interaction, the flavour state is created as a coherent superposition of the mass eigenstates at time t = 0, |ν(t = 0) = |να  =

n 

∗ Uαi |νi .

(2.6)

i=1

In vacuum, the neutrino mass states are eigenstates of the free propagation Hamilto3 nian. Assuming a plane  wave solution, the neutrino mass states evolve with a factor

e−i Ei t , where E i = 1

p 2 + m i2 is the energy of the ith mass eigenstate. Therefore,

The description given here is for oscillations in vacuum. Conversely, the mass states are a combinations of the flavour states. 3 A more complete treatment is done via the wavepacket approach; however, this leads to the same result as the plane wave assumption [18]. 2

2.4 Neutrino Oscillation Parameter Overview

|ν(t) =

n 

∗ −i E i t Uαi e |νi  =

i=1

7 n 

∗ −i E i t Uαi e

n 

∗ Uαβ |νβ ,

(2.7)

β=1

i=1

and the probability of detecting this neutrino in a state β at time t is given by, 2  n   ∗ −i E i t   P(να → νβ ) = |νβ |ν(t)| =  Uβi Uαi e  . 2

(2.8)

i=1

In  general, neutrinos are produced in an ultra-relativistic state. By expanding E i = p 2 + m i2 ≈ E + m i2 /2E (using E p), the oscillation probability can be written as [19], P(να → νβ ) = δαβ − 4

n 

∗ Re[Uαi Uβi Uα∗ j Uβ j ] sin2

i< j

+2

n 

∗ Im[Uαi Uβi Uα∗ j Uβ j ] sin





i< j

m 2ji L



4E m 2ji L 2E

,

(2.9)

where m 2ji = m 2j − m i2 is the mass splitting and L ct is the distance travelled by the neutrino. In the case of antineutrino oscillations, U is replaced by U ∗ which results in a sign change in the final term of Eq. 2.9.

2.4 Neutrino Oscillation Parameter Overview Since the discovery of neutrino oscillations 20 years ago, neutrino oscillation experiments have now moved into a new era: precision measurements of the parameters in the PMNS matrix and neutrino mass-squared splittings. The PMNS matrix can be described by three mixing angles, θ12 , θ13 , θ23 and a CPviolating phase δCP . It is useful to parametrise the PMNS matrix with these mixing angles and rewrite it as4 : ⎛ ⎞⎛ ⎞⎛ ⎞ 1 0 0 c13 c12 s12 0 0 s13 e−iδCP 0 1 0 ⎠ ⎝−s12 c12 0⎠ Uα j = ⎝0 c23 s23 ⎠ ⎝ iδCP 0 −s23 c23 0 0 1 −s13 e 0 c13     Atmospheric

4

Reactor

Solar

The additional case that the neutrino could be a Majorana particle has not been included here. In this case, it is not possible to re-phase the neutrino fields and so there are a total of 3 CP-violating phases in addition to the 3 mixing angles. The Majorana matrix does not affect neutrino oscillation probabilities, and is a unit matrix in the case neutrinos are Dirac fermions [19].

8

2 Overview of Neutrino Properties

where ci j = cos θi j and si j = sin θi j . In this parametrisation, the PMNS matrix has been decomposed into a product of the Atmospheric, Reactor and Solar matrices. These are three different regimes of neutrino oscillation which can be measured in experiments. There are several interesting features to note about neutrino oscillations: • Oscillations are only possible if the neutrino masses are not degenerate (i.e. m 2ji = 0) and at least one of the mass states is not zero. Moreover, neutrino oscillations are sensitive to the mass squared difference rather than the absolute masses. • The amount of mixing depends on three mixing angles, θ12 , θ13 , θ23 . In the case of θi j = 0, there would be no oscillations. Maximal mixing occurs for θ = π4 . • Oscillations depend on L/E. In an experiment this can be controlled either by adjusting the energy or distance between a source and detector. In many experiments, oscillations between two-neutrinos are a good approximation due to the order of magnitude difference in mass-squared splittings. In this case, there will be no sensitivity to the CP-violating phase and oscillations for neutrinos and antineutrinos would be identical and the probability of a neutrino with flavour να oscillating to νβ is given by,

m 2 [eV2 ] · L[km] P(να → νβ ) = P(ν¯α → ν¯β ) = sin (2θ) sin 1.27 · , 4E[GeV] (2.10) 2

2

where the equation uses SI units. It is also useful to write this as a survival probability: P(να → να ) = 1 − P(να → νβ ).

2.4.1 Atmospheric Mixing Parameters Atmospheric neutrinos are produced from the decays of pions and kaons created by cosmic rays and nucleons bombarding the Earth’s atmosphere. The energy of atmospheric neutrinos have been observed to range from ∼100 MeV to the PeV scale and travel distances ∼10 km to 104 km [20]. Super-Kamiokande measured the atmospheric mass splitting to be m 2atm ∼ 2.3 × 10−3 eV2 with a mixing angle close to 45◦ [21] by measuring atmospheric muon-neutrino disappearance. Accelerator experiments can test neutrino oscillations by creating a beam of neutrinos in a certain energy range by colliding protons against a target. Using a dedicated neutrino beam, the OPERA experiment demonstrated the appearance of tau neutrinos in a beam of muon neutrinos. This confirmed that muon neutrinos were oscillating into tau neutrinos [22] for an L/E corresponding to the atmospheric mass splitting.

2.4 Neutrino Oscillation Parameter Overview

9

2.4.2 Solar Mixing Parameters Measurements from studying the solar neutrino flux could be used to infer the mass splitting of these oscillations. These results gave m 2solar ∼ 7.5 × 10−5 eV2 [14]. KamLAND [23] was able to confirm this by measuring the electron antineutrino flux from a number of nuclear reactors with a L/E sensitive to m 2 ∼ 1 × 10−5 . They were able to conclusively show neutrino oscillations with a mass splitting m 2solar ∼ 8 × 10−5 eV2 with a mixing angle of around 33◦ .

2.4.3 Reactor Mixing Parameters Measurements of the final mixing angle were made by utilising the intense flux of electron antineutrinos from reactors. The Daya Bay [24], RENO [25] and Double Chooz [26] experiments all published results in 2012 measuring the disappearance of ν¯e at L ∼ 1 km and found a mixing angle θreactor ∼ 9◦ .

2.4.4 Summary of Neutrino Oscillation Parameters Putting the neutrino oscillation results together, there are two mass splittings which differ by a factor of 30, m 2solar = m 221 ∼ 7.5 × 10−5 eV2 and m 2atm = m 232 ∼ 2.3 × 10−3 eV2 . It is also determined from the effect of the high matter density in the Sun on solar neutrino oscillations [27, 28] that the ν2 state is heavier than the ν1 state. It is currently not known if the ν3 state is the heaviest (normal ordering) or the lightest state (inverted ordering). This is known as the neutrino mass hierarchy/ordering and experiments such as NOvA [29] and DUNE [30] were designed to measure this. Figure 2.1 shows the neutrino mass-squared splittings with normal and inverted ordering. The determination of δCP is currently being investigated. T2K have reported δCP to be non-zero (or π) at 3σ [32] and future experiments to come online that aim for a 5σ discovery of a CP-violating value include DUNE [30] and Hyper-Kamiokande [33]. Discovery of a CP-violating value of δCP could provide insight into our understanding of the matter-antimatter asymmetry produced in the early universe. A summary of the neutrino oscillation parameters are given in Table 2.1.

2.4.5 Short-Baseline Oscillations The LSND experiment was a neutrino oscillation experiment that operated at Los Alamos National Lab from 1993 to 1998 [34]. The detector consisted of a large tank

10

2 Overview of Neutrino Properties

Fig. 2.1 A cartoon of the neutrino mass ordering with normal ordering shown on the left and inverted ordering on the right. The colours show the probability of finding each flavour in each c 2013 IOP Publishing, reproduced with permission, all rights mass state. Image from Ref. [31], reserved Table 2.1 A summary of the 3ν oscillation parameters. Table parameters are obtained from Ref. [14] Parameter Normal ordering Inverted ordering sin2 θ12 sin2 θ23 sin2 θ13 m 221 m 232

0.307±0.013 0.546±0.021 (2.20±0.07) × 10−2 (7.53±0.18) × 10−5 eV2 (2.453±0.033) × 10−3 eV2

0.307±0.013 0.539±0.022 (2.20±0.07) × 10−2 (7.53± 0.18) × 10−5 eV2 (-2.536±0.034) × 10−3 eV2

of mineral oil lightly doped with scintillator. Charged daughter particles from the neutrino interaction produced primarily scintillation light with a smaller fraction of Cherenkov light which could be detected by a series of PMT arrays surrounding the detector. LSND observed an anomalous excess of events in the ν¯μ → ν¯e channel consistent with a mass splitting of 1 eV2 , a value that is not compatible with the 3ν oscillation parameters. Precision measurements from the decay width of the Z 0 resonance [35] show that the number of active light neutrino states are consistent with there being three neutrinos. Therefore, this type of excess could not be explained by introducing

References

11

another light active neutrino and could hint at neutrino mixing with an additional sterile5 neutrino state. The MiniBooNE experiment [36] was designed to test the result from LSND. The MiniBooNE detector was filled with pure mineral oil and detected the Cherenkov light produced by the charged daughter particles from the neutrino interaction. The experiment operated in an independent beamline at Fermilab, Chicago but with a similar L/E ∼ 1 eV2 . MiniBooNE operated from 2002 to 2019 and reported an anomalous excess of events with a 4.8σ difference with respect to the data at low neutrino energy and high scattering angle [37]. The MicroBooNE experiment (which started operating in 2016) is the successor to the MiniBooNE experiment. It is located in the same beamline as the MiniBooNE experiment with a similar baseline. One of the main drawbacks of the MiniBooNE experiment was that it could not easily distinguish photon-induced from electroninduced electromagnetic showers. Photon-induced showers were one of the largest backgrounds for the experiment. MicroBooNE is a LArTPC detector which has the ability to resolve the particles from a neutrino interaction to millimetre resolution as well as having excellent calorimetry. These features allow it to separate photon-induced and electron-induced electromagnetic showers which will be used to determine the nature of the excess observed by MiniBooNE.

2.4.6 Oscillations with Electron Neutrinos Electron-neutrino appearance is the golden channel for answering the main questions in neutrino oscillation experiments that have been mentioned in this Chapter, including: whether neutrinos violate the CP symmetry, determining the mass ordering and investigating whether sterile neutrinos exist. Therefore, it is crucial to have a good understanding of electron-neutrino interactions. This thesis contributes to this goal by providing a measurement of the electron neutrino cross section on an argon nucleus using the MicroBooNE detector and the off-axis NuMI beam.

References 1. Pauli W Pauli letter collection: letter to Lise Meitner. Typed copy 2. Griffiths D (2020) Introduction to elementary particles, 2nd edn. Wiley, New York 3. Horejsi J (1993) Introduction to electroweak unification: standard model from tree unitarity. World Scientific, Singapore 4. Wu CS, Ambler E, Hayward RW, Hoppes DD, Hudson RP (1957) Experimental test of parity conservation in beta decay. Phys Rev 105(4):1413–1415 5. Goldhaber M Grodzins L, Sunyar AW (1958) Helicity of neutrinos. Phys Rev 109(3):1015– 1017 5

The term sterile refers to a neutrino that does not interact via the weak force but can possibly mix with the active (weakly-interacting) neutrinos.

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2 Overview of Neutrino Properties

6. (2006) Electroweak interactions. In: Nuclear and particle physics. Wiley, New York, pp 181– 216 7. Sudarshan ECG, Marshak RE (1958) Chirality invariance and the universal fermi interaction. Phys Rev 109(5):1860–1862 8. Feynman RP, Gell-Mann M (1958) Theory of the fermi interaction. Phys Rev 109(1):193–198 9. Reines F, Cowan CL, Harrison FB, McGuire AD, Kruse HW (1960) Detection of the free antineutrino. Phys Rev 117(1):159–173 10. Danby G, Gaillard J-M, Goulianos K, Lederman LM, Mistry N, Schwartz M, Steinberger J (1962) Observation of high-energy neutrino reactions and the existence of two kinds of neutrinos. Phys Rev Lett 9(1):36–44 11. Kodama K et al (2001) Observation of tau neutrino interactions. Phys Lett B 504(3):218–224 12. Zuber K (2020) Neutrino physics, 3rd edn. Series in high energy physics, cosmology & gravitation. CRC Press 13. Giunti C, Kim CW (2007) Fundamentals of neutrino physics and astrophysics. Oxford University Press 14. Zyla P et al (2020, 2021) Review of particle physics. PTEP 2020(8):083C01 15. Pontecorvo B (1958) Inverse beta processes and nonconservation of lepton charge. Sov Phys JETP 7:172–173 16. Pontecorvo B (1967) Neutrino experiments and the problem of conservation of leptonic charge. Zh Eksp Teor Fiz 53:1717–1725 17. Maki Z, Nakagawa M, Sakata S (1962) Remarks on the unified model of elementary particles. Prog Theor Phys 28:870–880 18. Smirnov AY (2017) Solar neutrinos: oscillations or no-oscillations? arXiv: 1609.02386 [hepph] 19. Giganti C, Lavignac S, Zito M (2018) Neutrino oscillations: the rise of the PMNS paradigm. Prog Part Nucl Phys 98:1–54 20. Richard E et al (2016) Measurements of the atmospheric neutrino flux by Super-Kamiokande: energy spectra, geomagnetic effects, and solar modulation. Phys Rev D 94(5):052001 21. Fukuda Y et al (1999) Measurement of the flux and zenith-angle distribution of upward throughgoing muons by Super-Kamiokande. Phys Rev Lett 82(13):2644–2648 22. Agafonova N et al (2010) Observation of a first ντ candidate event in the OPERA experiment in the CNGS beam. Phys Lett B 691(3):138–145 23. Eguchi K et al: First results from KamLAND: evidence for reactor antineutrino disappearance. Phys Rev Lett 90(2) 24. An FP et al (2012) Observation of electron-antineutrino disappearance at Daya Bay. Phys Rev Lett 108(17):171803 25. Ahn JK et al (2012) Observation of reactor electron antineutrinos disappearance in the reno experiment. Phys Rev Lett 108(19):191802 26. Abe Y et al (2012) Reactor ν¯ e disappearance in the Double Chooz experiment. Phys Rev D 86(5) 27. Wolfenstein L (1978) Neutrino oscillations in matter. Phys Rev D 17(9):2369–2374 28. Mikheyev SP, Smirnov AY (1985) Resonance amplification of oscillations in matter and spectroscopy of solar neutrinos. Sov J Nucl Phys 42:913–917 29. Acero MA et al (2018) New constraints on oscillation parameters from νe appearance and νμ disappearance in the NOvA experiment. Phys Rev D 98(3) 30. Abi B et al (2020) Long-baseline neutrino oscillation physics potential of the DUNE experiment. Eur Phys J C 80(10):978 31. King SF, Luhn C (2013) Neutrino mass and mixing with discrete symmetry. Rep Prog Phys 76(5):056201 32. Abe K et al (2020) Constraint on the matter-antimatter symmetry-violating phase in neutrino oscillations. Nature 580(7803):339–344 33. Abe K et al (2018) Hyper-Kamiokande design report. arXiv: 1805.04163 [physics.ins-det] 34. Hill JE (1995) An alternative analysis of the LSND neutrino oscillation search data on ν¯ μ ν¯ e . Phys Rev Lett 75(14):2654–2657

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35. (2006) Precision electroweak measurements on the z resonance. Phys Rep 427(5):257–454 36. Aguilar-Arevalo A et al (2009) The MiniBooNE detector. Nucl Instrum Methods Phys Res Sect A: Accel Spectrometers Detect Assoc Equip 599(1):28–46 37. Aguilar-Arevalo AA et al (2021) Updated MiniBooNE neutrino oscillation results with increased data and new background studies. Phys Rev D 103(5):052002

Chapter 3

Neutrino Interactions

Chapter 2 gave an overview of neutrino properties and how we can measure them via oscillations. Most of these measurements crucially depend on understanding the nature of neutrino interactions. This chapter will go over the physics of neutrino interactions that are relevant for the MicroBooNE experiment which studies neutrinos interacting with argon at energies in the range from a few hundred MeV to a few GeV. The chapter will conclude with an overview of electron-neutrino interaction measurements which provide the context for the measurements presented in this thesis. Additional resources on the neutrino interaction physics and measurements described in this chapter can be found in Refs. [1, 2].

3.1 Importance of Neutrino Cross Sections in Oscillation Experiments Accelerator neutrino oscillation experiments are typically performed by measuring the event rate in one or many detectors along a neutrino beam. In the case of a να → να oscillation disappearance experiment, the rate observed at the far detector FD , is given by: (FD), Nobs FD Nobs (E ν,obs )

   FD FD FD Posc (E ν ) ×  (E ν ) × σ(E ν ) × D (E ν,obs , E ν ) ×  (E ν ) = FD , d E ν + Nbg

(3.1) where Posc (E ν ) is the oscillation probability, FD (E ν ) is the total neutrino flux, σ(E ν ) is the cross section, D FD (E ν,obs , E ν ) describes the detector response at the FD far detector, FD (E ν ) is the efficiency and Nbg (E ν,obs ) is the expected background © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 K. V. J. Mistry, Exploring Electron-Neutrino–Argon Interactions, Springer Theses, https://doi.org/10.1007/978-3-031-19572-3_3

15

16

3 Neutrino Interactions

prediction at the far detector1 . The energy E ν,obs is the observed (reconstructed) energy at the far detector and E ν is the true neutrino energy. A challenge for these experiments is that E ν,obs is not directly measured, it is calculated using observables from the detector. Missing energy from particles being created below the detection threshold, exiting particles, mis-reconstruction, the choice of target, and background contamination can further complicate this. In addition, nuclear effects can also alter the size and shape of the cross section as well as the kinematics and composition of the particles produced from the initial interaction. All these factors will directly affect the measured neutrino energy requiring the use of model-derived corrections to recover the true energy. Crucially, mis-modelling these effects can lead to large uncertainties which can reduce the sensitivities of these experiments or even introduce biases. A common method employed to reduce flux and cross section uncertainties in an oscillation experiment is to measure the event rate at a detector close to the source of the neutrinos. This detector is known as a near detector (ND). The event rate at the ND is given by:   ND (E ν,obs ) = Nobs

 ND (E ν ) × σ(E ν ) × D ND (E ν,obs , E ν ) × ND (E ν ) d E ν

ND + Nbg .

(3.2) However, while taking the ratio of the far detector and near detector can cause a cancellation of some uncertainties such as the modelling of flux, cross section, detector response and efficiencies, this cancellation is not perfect for several reasons: • Near detectors are not always built to be exactly the same as the far detector. In this case, the neutrino target material can be different as well as the detector systematic uncertainties. • The neutrino flux prediction at the near and far detector is not the same. This results in a different estimation in the hadron production and the neutrino beamline simulation uncertainties at each detector. • The efficiencies can vary if the performance of each detector is different. As a result, cross section measurements have an important role in neutrino oscillation experiments: they pin down the physics of neutrino interactions and reduce their associated uncertainties in the models that are used. The next sections will focus on describing the main elements of how neutrino interactions are modelled in the accelerator neutrino energy range.

1

While not shown here for simplicity, the cross section, detector response and efficiency can also depend on several variables such as the outgoing lepton energy/angle which are also integrated over.

3.2 Neutrino Interactions

17

3.2 Neutrino Interactions Neutrinos can interact with a target nucleon, lepton or nucleus via charged current or neutral current (NC) weak interactions. The cross section of these interactions is a function of several different parameters including the incident neutrino energy. In the energy range of a few hundred MeV to a few GeV, a number of distinct interaction mechanisms contribute as shown in Fig. 3.1. These mechanisms can be broken down into three main types: Quasi-Elastic (QE), Resonant (RES) and Deep Inelastic Scattering (DIS). QE interactions contribute most in the region from 100 MeV - 2 GeV. Beyond this, resonant interactions are important up-to a few GeV where DIS starts to dominate. The linear dependence of the cross section when reaching the region where DIS becomes the main mode of interaction is due the interaction becoming a scattering off of point-like quarks [3]. For antineutrinos, the cross section is roughly a factor of three smaller than the neutrino cross section due to helicity suppression. Overall, there have been fewer measurements of antineutrinos compared to neutrinos. In this section, a description of the main interaction processes for CC and NC neutrino interactions on free nucleons is first given. This is followed by further extensions to these models which are introduced to account for nuclear effects arising from the complex interactions of neutrinos and their products inside the nucleus.

3.2.1 Neutrino Generators To simulate neutrino interactions, neutrino oscillation experiments use neutrino generators which implement models for neutrino interactions by stitching together the

Fig. 3.1 The total (left) neutrino and (right) antineutrino cross section divided by neutrino energy as a function of this energy overlaid with data from several experiments described in Ref. [3]. The predictions for the total, QE, RES and DIS are shown by the solid, dashed, dot-dashed and dotted lines respectively and are provided by the NUANCE generator [4]. Reprinted figure with permission from Ref. [3]. Copyright 2012 by the American Physical Society

18

3 Neutrino Interactions

different interaction modes and nuclear effects. Widely used generators include GENIE [5], NEUT [6], NuWro [7], GiBUU [8] and NUANCE [4]. Accelerator neutrino oscillation experiments typically use generators that have functionality to handle an input flux prediction and detector geometry specific to their experiment. In addition, they require an interface to propagate the cross section uncertainties from the generators to the simulation. The measurements presented in this thesis primarily employ the GENIE generator but also use the NuWro generator for validation purposes. The description of the neutrino interactions in this section will be organised by the models implemented in these generators.

3.2.2 Quasi-Elastic Scattering Quasi-elastic scattering is the dominant neutrino interaction mechanism in the energy range between ∼(0.1 - 2) GeV. For charged current quasi-elastic (CCQE) interactions on a free nucleon, this is given by: νl + n → l − + p ν¯l + p → l + + n,

(3.3)

where l = e, μ, τ . The cross section of this type of interaction was described by Llewellyn-Smith and the mathematical formulation of the cross section can be found in Ref. [9]. The CCQE cross section depends on several form factors which encompass information about the internal structure of the nucleons. These include the vector, F1 and F2 , and axial, FA and FP , form factors. The vector form factors can be measured precisely over a wide range of fourmomentum transfer squared, Q 2 , from electron scattering experiments on protons and deuterium. These form factors can be translated to neutrino QE scattering due to the conserved vector current (CVC) and isospin symmetry. A common parametrisation for these form factors used in neutrino generators is the BBBA05 parametrisation [10]. The axial form factors can only be determined from neutrino scattering with the vast majority of measurements consisting of muon neutrino QE scattering. A dipole form for the axial form factors is often assumed, F(Q 2 ) ∝ F(0)/(1 + Q 2 /C 2 )2 ,

(3.4)

where C is a constant and is commonly expressed as a mass similar in size to the mass of a nucleon and F(0) is the value of the form factor at Q 2 = 0 [11]. Using this dipole form, the axial form factor can be written as FA = g A /(1 + Q 2 /M A2 ), where M A is the axial mass and F(0) = g A = 1.2671 [3, 12], which is determined from nucleon and nuclear beta decay.

3.2 Neutrino Interactions

19

The pseudo-scalar axial form factor is determined through the partially conserved axial current (PCAC) hypothesis which relates pion-nucleon interactions to nuclear beta decay [13] and is given by FP = 2M N2 FA /(Mπ2 + Q 2 ), where M N is the mass of the nucleon in the interaction and Mπ is the pion mass.

3.2.3 Resonant Scattering and Pion Production Resonant Single Pion Production If a neutrino has enough energy, neutrinos can inelastically scatter off a nucleon and excite it into a baryon resonance, N ∗ , which subsequently decays on a short time scale. The most common decay mode is to a nucleon and a single pion. Other less-common decays of these baryon resonances include decays to photons, multiple pions, other mesons such as K , η, ρ. At energies close to 1 GeV, the most common resonance produced is the (1232) state. Example CC decay channels to single pions of this resonance include: νl + p → l − + p + π + ,

ν¯l + p → l + + p + π − ,

νl + n → l − + p + π 0 , ν¯l + p → l + + n + π 0 , νl + n → l − + n + π + , ν¯l + n → l + + n + π − .

(3.5)

Similarly there are four NC decay channels for neutrinos and antineutrinos: νl + p → νl + p + π 0 , ν¯l + p → ν¯l + p + π 0 , νl + p → νl + n + π + , ν¯l + n → ν¯l + n + π 0 , νl + n → νl + n + π 0 , ν¯l + n → ν¯l + n + π 0 , νl + n → νl + p + π − , ν¯l + n → ν¯l + p + π − .

(3.6)

The resonances that produce π 0 , especially the NC interactions which lack an easily identifiable charged lepton, can form significant backgrounds for accelerator neutrino oscillation experiments that search for νμ → νe appearance. This is because the π 0 can decay to two photons which can be mis-identified as an electron induced shower, which is the key characteristic of electron neutrino interactions [3]. There are several resonant scattering models used in the neutrino generators in this thesis. This includes the Rein-Sehgal model and more recent updates to this model via the Kuzmin-Lubushkin-Naumov (KLN) [14] and Berger-Sehgal [15, 16] models. The KLN model adds the outgoing lepton mass and spin for single pion production. The Berger-Sehgal model includes data from total and differential pion cross sections. Another implementation of resonant interactions include the Adler-Rarita-Schwinger model where it calculates (1232) resonance explicitly and includes a smooth transition to DIS at 1.6 GeV [17].

20

3 Neutrino Interactions

Coherent Pion Production Neutrinos can also interact coherently with a nucleus. In these interactions, neutrinos transfer a negligible amount of energy to the target nucleus but produce a forwardboosted pion. Examples of these interactions are: CC : νl + A → l − + A + π + , ν¯l + A → l + + A + π − , NC : νl + A → νl + A + π 0 ,

ν¯l + A → ν¯l + A + π 0 .

(3.7)

The cross sections from these type of interactions are sub-dominant compared to the standard resonant pion production in the energy range of a few hundred MeV to couple GeV [3]. Examples of models implemented in the neutrino generators used in this thesis include Rein-Sehgal [18] and Berger-Sehgal [19].

3.2.4 Deep Inelastic Scattering For energies above several GeV, neutrinos can resolve the internal structure of a nucleon and interact directly with a quark. This is known as deep inelastic scattering. While there is no precise way based on the kinematics of the neutrino interaction to determine when the interaction switches from the resonance region to the DIS region, usually energies above ∼(3–4) GeV are used. This type of interaction results in the nucleus breaking apart and is dominant for energies above several GeV. All neutrino generators in this thesis use the Bodek-Yang model for these interactions [20, 21].

3.3 Nuclear Effects The CCQE, CCRES and CCDIS interaction modes assume the neutrino interaction happens on free nucleons. These assumptions work reasonably well for neutrino experiments that use light targets such as hydrogen or deuterium. However, measurements using heavy targets such as carbon and argon are subject to nuclear effects and the free-nucleon assumption often breaks down. These effects can make it impossible to identify the interaction mode by which the neutrino interacted. In addition, nucleons which have many more neutrons compared to protons (or vice versa) could introduce different nuclear effects for neutrinos compared to antineutrinos. This can be important for experiments such as DUNE [22] that want to precisely measure the difference in interaction rates between neutrinos and antineutrinos. Precisely understanding the impact of nuclear effects is non trivial. There are many nucleons inside the nucleus which can form a complex many-body system. There can be correlations between one or many nucleons, and a particle produced in

3.3 Nuclear Effects

21

the initial interaction can re-scatter, produce more particles or be absorbed before it exits the nucleus. There are a number of models each with their own approach to account for these effects. Implementing them can be challenging especially in terms of maintaining the overall consistency of the neutrino-nucleus interaction. This section breaks down the main elements involved in modelling neutrino interactions with a nucleus.

3.3.1 Neutrino-Nucleus Interactions To describe quasi-elastic neutrino interactions with a realistic nucleus, one approach is to use the so-called impulse approximation (IA). This model was originally developed for electron scattering on nuclei and was carried over to neutrino scattering. In the IA, two assumptions are made [23]: • The neutrino has a momentum that is large enough such that the target nucleus is seen as a collection of individual nucleons. • The particles produced at the interaction vertex and the recoiling (A - 1)-nucleon system evolve independently of one another. With these approximations, the neutrino scattering is essentially described as an incoherent sum of elementary processes involving one nucleon as shown in Fig. 3.2. In the IA, information about the Fermi motion in the nucleus is incorporated into a spectral function, SF(p,E), which gives the probability to find a nucleon with energy E. There are various forms that can be assumed for the spectral function. The global relativistic Fermi gas (RFG or GFG) model treats the nucleons as if they are in a noninteracting constant potential. All nucleons in this potential are filled with energies from the ground state upwards where the highest momentum state is given by the Fermi momentum, k f . The local fermi gas (LFG) model extends the RFG model by considering the local positions of the nucleons within the nucleus of radius, r , by

Fig. 3.2 A diagram of neutrino scattering on a free nucleon on the left which is then modified to the the scheme on the right in the impulse approximation. In this scheme the cross section for a neutrino interaction with a nucleus is given by the incoherent sum of processes involving one nucleon. Adapted figure with permission from Ref. [23]. Copyright 2012 by the American Physical Society

22

3 Neutrino Interactions

using a local nuclear density, ρ(r ), to model the potential. In these approaches, the nucleons cannot move into a state that is already occupied (known as Pauli blocking). To release a nucleon, the neutrino must transfer enough energy to the nucleon and exceed the Fermi momentum for the reaction to occur.

3.3.2 Nucleon-Nucleon Correlations Models in the IA on their own are not enough to describe interactions with a nucleus since they do not take into account nucleon-nucleon correlations. These correlations, as demonstrated in electron-nucleus scattering experiments [24, 25], alter the initial state of the nucleon which modifies the measured cross section. Correlations between nucleons can lead to them forming bound states inside the nucleus. These bound states are split into three categories based on their region in the nuclear potential V (r ): short range correlations (SRCs), 2-π exchange and 1-π exchange as depicted in Fig. 3.3.

Fig. 3.3 A diagram of the nuclear potential which is split into three regions. The variable x denotes the inter-nucleon distance in units of the pion Compton wavelength, κ−1 ∼ 1.4 fm. 1-π exchange is given by x ≥ 1.5κ−1 , 2-π exchange is given by 0.7κ−1 ≤ x ≥ 1.5κ−1 and SRC is given by c 1956, x ≤ 0.7κ−1 . Figure from Ref. [26]. With permission, adapted from Ref. [27] Copyright  c 2007, Oxford University Press Oxford University Press and Ref. [28] Copyright 

3.3 Nuclear Effects

23

Fig. 3.4 MiniBooNE νμ CC cross section on 12 C compared to predictions without MEC (red dashed), with MEC (green solid) and Martini et al. prediction which implements an unrealistic axial mass, M A = 1.35 GeV to give better agreement with the data (dot-dash blue) [33]. Reprinted figure with permission from Ref. [34]. Copyright 2011 by the American Physical Society

Meson exchange current (MEC) is an overall term used to describe states with n nucleons bound via the exchange of virtual mesons. MEC contributes mostly in the energy region between QE and RES. This effect has only recently been proposed to explain the sizeable enhancement in the measured CCQE cross section in experiments such as MiniBooNE. Figure 3.4 shows MiniBooNE data on 12 C compared to predictions with and without MEC. In this case, 2 nucleon correlations are used. These are also known as 2 particle 2 hole (2p2h) interactions due to the participation of 2 nucleons in the interaction. There are several implementations of MEC used in the neutrino generators in this thesis. This includes an empirical MEC [29] model that uses fits to MiniBooNE data [30], a Nieves model [31] and a Transverse Enhancement model [32]. Figure 3.4 shows that introducing 2p2h alone does not completely resolve the data to prediction differences. An additional correction known as the random phase approximation (RPA) is needed to give a good description. RPA accounts for the average effect of microscopic interactions in a many-body strongly interacting system. It results in a change in the effective electroweak coupling strength compared to the free nucleon value and is dominant in regions of low Q 2 [35, 36]. A model using the combination of MEC and RPA effects compared to MiniBooNE data is shown in Fig. 3.5. The combination of these models give good agreement with the data.

3.3.3 Final State Interactions Particles that are produced in a neutrino interaction with a nucleus can re-scatter inside the nucleus where they can produce other hadrons, knock out other nucleons or be absorbed. Pictorially shown in Fig. 3.6, these effects are known as final state interactions (FSI). This can alter the multiplicities, momenta and direction of the outgoing particles, and are particularly challenging to model. The intranuclear

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Fig. 3.5 The double differential cross section, in the range from 0.8 < cos θμ < 0.90, on 12 C as a function of the outgoing muon kinetic energy compared to a number of predictions. The orange line shows the the contribution to the full model from multinucleon correlations. The green model shows a prediction that includes MEC, RPA effects and a reasonable axial mass, M A = 1.049 GeV and gives the best agreement with the data. Reprinted from Ref. [36], Copyright Elsevier with permission

cascade (INC) is one example of an FSI model which describes the hadron-nucleus cross sections in the intranuclear medium [37]. The mean free path of the hadrons as they traverse the nucleus is given by: λ=

1 , σn

(3.8)

where σ is the characteristic hadron-nucleon scattering cross section and n is the density of nucleons [12]. It should also be noted that FSI can also affect the outgoing lepton due to the electric field of the nucleus. These corrections are known as Coulomb corrections and can alter the momentum of the outgoing lepton in CC interactions [35]. Implementations of FSI used in this thesis include the hA [38] and hA2018 [39] models. These are empirical models that use measurements of the total cross section of pions and nucleons rather than explicitly calculating the cascade of hadronic interactions [40]. In these predictions, no nuclear medium effects are applied to pions, however, they are included for nucleons. An alternative implementation for FSI is provided by the Salcedo-Oset [41] model.

3.4 Inclusive and Exclusive Measurements

25

Fig. 3.6 A diagram showing final state interactions after an initial neutrino-nucleus interaction. Figure from Ref. [26], licensed under CC-BY-4.0

3.4 Inclusive and Exclusive Measurements Measurements of CC neutrino cross sections can broadly be categorised into two types, inclusive and exclusive. In the case of an exclusive measurement, a requirement on the particles accompanying the neutrino interaction is applied. For example, an exclusive measurement may require there is exactly one proton accompanying the lepton. For early experiments where the targets consistent of light nuclei such as deuterium, specific neutrino interaction modes such as CCQE or CCRES were well-defined. However, as discussed in this chapter, modern experiments tend to use heavier targets which introduce nuclear effects. With the increased understanding of FSI and nuclear interactions, exclusive measurements now focus on particular topologies in an ongoing effort to improve theoretical models. For inclusive measurements, no requirements are made on the presence or absence of additional particles accompanying the outgoing lepton from the interaction. This signature includes all neutrino interaction modes and limits the impact of FSI which mostly affects the hadrons from the interaction. In addition, inclusive measurements are important for understanding the overall interaction rate in oscillation experiments where there can be migrations across exclusive channels.

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3.5 Electron Neutrino Cross Section Measurements Measurements of neutrino cross sections in the GeV range are dominated by measurements of muon neutrino interactions due to the availability of these neutrinos in modern neutrino experiments. Experiments that rely on precision measurements of the electron neutrino and antineutrino cross section such as MicroBooNE, the SBN programme [42], NOvA [43], T2K [44], DUNE [22] and Hyper-Kamiokande [45] benefit from high precision measurements of electron neutrino interactions on various targets. For experiments in the energy regime of ∼1 GeV, significant differences are expected in the muon neutrino and electron neutrino cross sections. Theoretical predictions of the ratio of the cross sections in energy and angle using a 12 C target are shown in Fig. 3.7 [46]. Differences in the predicted cross section can be as large as 50% at low energy and angles and up to 25% at low energy and high angles of the outgoing lepton, although it should be noted that these are regions where differences in the lepton mass have an important contribution. Studies have also shown there can be differences of up-to 10% in the electron neutrino and muon neutrino CCQE cross section at low energy due to radiative corrections which are not typically accounted for in neutrino generators. Additional differences (although typically accounted for) are introduced due to differences in

Fig. 3.7 The ratio of the calculated electron neutrino and muon neutrino cross section on 12 C using a continuum RPA approach. Reprinted figure with permission from Ref. [46]. Copyright 2019 by the American Physical Society

3.5 Electron Neutrino Cross Section Measurements

27

the lepton mass and due to the presence of the pseudo-scalar form factor which is more significant for muon neutrinos [11]. Uncertainties of this magnitude would have a significant impact on the sensitivities of experiments such as DUNE and Hyper-Kamiokande emphasising the need for dedicated electron neutrino measurements.

3.5.1 Gargamelle The Gargamelle experiment was the first experiment to publish an electron neutrino and antineutrino cross section measurement in 1973 [47]. The detector employed a heavy liquid bubble chamber. The liquid used was freon, CF3 Br, which has a short radiation length (X 0 = 11 cm) and allowed the identification of electrons and positrons by identifying bremsstrahlung and spiralling tracks in a magnetic field. The measurement was made for the following processes: νe + N → e− + hadrons ν¯e + N → e+ + hadrons,

(3.9)

where it recorded a total of 45 electron and 7 positron events. This measurement was updated in 1978 with increased statistics recording a total of 200 electron and 60 positron events [48]. The signal definition included a 200 MeV energy threshold on the electron/positrons. The experiment found a linear cross section as a function of energy given by: νe : (0.7 ± 0.2)E ν × 10−38 cm2 /nucleon, ν¯e : (0.25 ± 0.07)E ν¯ × 10−38 cm2 /nucleon.

(3.10)

3.5.2 T2K The T2K experiment has published three electron neutrino cross section measurements to date. All three measurements were made using the ND280 [49] detector. This detector sits 280 m away and is off-axis by 2.5◦ relative to the J-PARC neutrino beam which is created from a 30 GeV proton beam impinging on a graphite target. The first CC differential electron neutrino cross section was made in 2014 using carbon as a target at energies ∼1 GeV [50]. This is one of the first electron neutrino cross section measurements in the modern era and the measurement is reported as the total flux-averaged cross section,

σ = 1.1 ± 0.10(stat) ± 0.18(syst) × 10−38 cm2 /nucleon,

(3.11)

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Fig. 3.8 The cross section for electron neutrinos and antineutrinos as a function of momentum and angle. This measurement is made in a limited phase-space where p >300 MeV/c and θ ≤45◦ . Figure from Ref. [52], licensed under CC-BY-4.0

which is in agreement with the measurement made by Gargamelle. In addition, T2K report the CCQE differential cross section as a function of the outgoing electron momentum, angle and Q 2 . These measurements were found to be in agreement with the GENIE and NEUT generators. In 2015, T2K reported the first measurement of the electron neutrino interaction rate using a water target using their pi-zero detector [51]. This detector was employed to measure the intrinsic νe in the beam for energies above 1.5 GeV and a mean energy of 2.7 GeV. The measurement was found to be consistent with the NEUT generator with a data to prediction ratio of 0.87 ± 0.33(stat) ±0.21(sys). More recently, in 2020, T2K has reported a measurement of the electron neutrino and antineutrino cross sections using both neutrino and antineutrino beams [52]. Figure 3.8 shows the differential cross section in electron momentum and angle (limited in the phase-space of p >300 MeV/c and θ ≤45◦ ). This measurement is the first electron neutrino cross section measurement using both neutrino and antineutrino mode fluxes and also the first CC-ν¯e cross section measurement since Gargamelle.

3.5.3 MINERvA The MINERvA experiment made the first direct measurement of electron neutrino CCQE scattering on hydrocarbon ((C8 H8 )n ) in the few GeV region [53]. MINERvA is on-axis to the NuMI beam which is created from a 120 GeV proton beam impinging on a graphite target. Since nuclear effects from using carbon as a target can affect the particles observed by the experiment, MINERvA uses a “CCQE-like” signal definition which requires the selected event to have a prompt electron or positron from the primary vertex plus any number of nucleons, but without any other hadrons or γ-ray conversions. MINERvA could not distinguish between electrons and positrons in their detector so they report the νe + ν¯e cross section with ν¯e forming 9% of the expected signal

3.5 Electron Neutrino Cross Section Measurements

29

Fig. 3.9 The differential cross section measurement from MINERvA on hydrogen/carbon as a function of electron energy and angle. The cross section measured is largely consistent with the GENIE generator. Reprinted figure with permission from Ref. [53]. Copyright 2016 by the American Physical Society

events. A total of 2205 selected CCQE-like candidates were used to calculate a differential cross section in electron production angle, electron energy and Q 2 . Figure 3.9 shows the differential cross sections in electron energy and angle compared to the GENIE neutrino generator.

3.5.4 ArgoNeuT The ArgoNeuT experiment recently reported in 2020 the first measurement of the electron neutrino cross section on argon as a target [54]. The data collected from this experiment uses the NuMI beamline and consists of 13 selected νe + ν¯e events where the average energy is 4.3 GeV for νe and 10.5 GeV for ν¯e . ArgoNeuT report the differential cross section as a function of outgoing electron angle as shown in Fig. 3.10 −36 cm2 . The and the total cross section of σ = (1.04 ± 0.38(stat)+0.15 −0.23 (syst)) × 10 measurement is found to be in agreement with the GENIE prediction.

3.5.5 Summary of Electron Neutrino Measurements This section summarised the current measurements of electron neutrino cross sections. Only six measurements exist to date, of which, only one is on argon. Measurements of the electron neutrino cross section on argon will be particularly important for the SBN programme and DUNE which are based on the LArTPC technology. This thesis will present two subsequent measurements on argon that increase the number of events observed by an order of magnitude.

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Fig. 3.10 The differential cross section measurement from ArgoNeuT on argon as a function of electron angle. The cross section measured is in agreement with the GENIE generator. Figure from Ref. [54], licensed under CC-BY-4.0

References 1. Zyla P et al (2020, 2021) Review of particle physics. PTEP 2020(8):083C01 2. Giunti C, Kim CW (2007) Fundamentals of neutrino physics and astrophysics. Oxford University Press 3. Formaggio JA, Zeller GP (2012) From eV to EeV: neutrino cross sections across energy scales. Rev Mod Phys 84(3):1307–1341 4. Casper D (2002) The nuance neutrino physics simulation, and the future. Nucl Phys B-Proc Suppl 112(1):161–170 5. Andreopoulos C, Bell A, Bhattacharya D, Cavanna F, Dobson J, Dytman S, Gallagher H, Guzowski P, Hatcher R, Kehayias P et al (2010) The GENIE neutrino Monte Carlo generator. Nucl Instrum Methods Phys Res Sect A: Accel Spectrometers Detect Assoc Equipment 614(1):87–104 6. Hayato Y (2002) Neut. Nucl Phys B-Proc Suppl 112(1):171–176 7. Golan T, Sobczyk J, and J. Zmuda (2012) NuWro: the Wroclaw Monte Carlo generator of neutrino interactions. Nucl Phys B-Proc Suppl 229–232:499; Neutrino 2010 8. Buss O, Gaitanos T, Gallmeister K, van Hees H, Kaskulov M, Lalakulich O, Larionov A, Leitner T, Weil J, Mosel U (2012) Transport-theoretical description of nuclear reactions. Phys Rep 512(1–2):1–124 9. Llewellyn-Smith C (1972) Neutrino reactions at accelerator energies. Phys Rep 3(5):261–379 10. Bradford R, Bodek A, Budd H, Arrington J (2006) A new parameterization of the nucleon elastic form factors. In: Nuclear physics B - proceedings supplements, vol 159, pp 127–132; Proceedings of the 4th international workshop on neutrino-nucleus interactions in the Few-GeV region 11. Day M, McFarland KS (2012) Differences in quasielastic cross sections of muon and electron neutrinos. Phys Rev D 86(5) 12. Gallagher H, Garvey G, Zeller G (2011) Neutrino-nucleus interactions. Annu Rev Nucl Part Sci 61(1):355–378

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13. Adler SL (1965) Consistency conditions on the strong interactions implied by a partially conserved axial-vector current. Phys Rev 137(4B):B1022-B1033 14. Kuzmin KS, Lyubushkin VV, Naumov VA (2004) Lepton polarization in neutrino-nucleon interactions. Phys Part Nucl 35:S133 15. Nowak JA (2009) Four momentum transfer discrepancy in the charged current π + ; production in the MiniBooNE: data vs. theory. AIP Conf Proc 1189(243) 16. Berger C, Sehgal LM () Lepton mass effects in single pion production by neutrinos. Phys Rev D 76(11):113004 17. Graczyk KM, D. Kiełczewska, P. Przewłocki, and Sobczyk JT (2009) C5A axial form factor from bubble chamber experiments. Phys Rev D 80(9):093001 18. Rein D, Sehgal L (2007) PCAC and the deficit of forward muons in π + production by neutrinos. Phys Lett B 657(4–5):207–209 19. Berger C, Sehgal LM (2009) Partially conserved axial vector current and coherent pion production by low energy neutrinos. Phys Rev D 79(5):053003 20. Bodek A, Yang UK (2003) Higher twist, ξw scaling, and effective LO PDFs for lepton scattering in the few GeV region. J Phys G: Nucl Part Phys 29(8):1899–1905 21. Yang U, Bodek A (2000) Studies of higher twist and higher order effects in NLO and NNLO QCD analysis of lepton-nucleon scattering data on F2 and R = σ L /σT . Eur Phys J C 13(2):241– 245 22. Abi B et al (2020) Long-baseline neutrino oscillation physics potential of the DUNE experiment. Eur Phys J C 80(10):978 23. Benhar O, Farina N, Nakamura H, Sakuda M, Seki R (2005) Electron and neutrino-nucleus scattering in the impulse approximation regime. Phys Rev D 72(5) 24. de Witt Huberts PKA (1990) Proton spectral functions and momentum distributions in nuclei from high-resolution (e,e’p) experiments. J Phys G: Nucl Part Phys 16(4):507–544 25. Rohe D et al (2004) Correlated strength in the nuclear spectral function. Phys Rev Lett 93(18):182501 26. Bathe-Peters L (2020) Studies of single-transverse kinematic variables for neutrino interactions on argon. FERMILAB-MASTERS-2020-03, M.S. thesis, Berlin Tech U., Harvard U 27. Taketani M (1956) Introduction. Nuclear forces and meson theory. Prog Theor Phys Suppl 3:1–12. https://academic.oup.com/ptps/article-pdf/doi/10.1143/PTPS.3.1/5189517/3-1.pdf 28. Weise W (2007) Yukawa’s pion, low-energy QCD and nuclear chiral dynamics. Prog Theor Phys Suppl 170:161–184. https://academic.oup.com/ptps/article-pdf/doi/10.1143/PTPS.170. 161/5234632/170-161.pdf 29. Katori T (2015) Meson exchange current (MEC) models in neutrino interaction generators. In: AIP conference proceedings, vol 1663, p 030001 30. Aguilar-Arevalo AA et al (2010) First measurement of the muon neutrino charged current quasielastic double differential cross section. Phys Rev D 81(9):092005 31. Schwehr J, Cherdack D, Gran R (2017) GENIE implementation of IFIC Valencia model for QE-like 2p2h neutrino-nucleus cross section. arXiv: 1601.02038 [hep-ph] 32. Bodek A, Budd H, Christy M (2011) Neutrino quasielastic scattering on nuclear targets. Eur Phys J C 71:1726 33. Martini M, Ericson M, Chanfray G, Marteau J (2010) Neutrino and antineutrino quasielastic interactions with nuclei. Phys Rev C 81(4):045502 34. Nieves J, Simo IR, Vacas MJV (2011) Inclusive charged-current neutrino-nucleus reactions. Phys Rev C 83(4):045501 35. Del Tutto M (2019) First measurements of inclusive Muon neutrino charged current differential cross sections on argon at 0.8 GeV average neutrino energy with the MicroBooNE detector. FERMILAB-THESIS-2019-05, Ph.D. dissertation, Oxford University Press 36. Nieves J, Ruiz Simo I, Vicente Vacas M (2012) The nucleon axial mass and the MiniBooNE quasielastic neutrino-nucleus scattering problem. Phys Lett B 707(1):72–75 37. Metropolis N, Bivins R, Storm M, Turkevich A, Miller JM, Friedlander G (1958) Monte Carlo calculations on intranuclear cascades. I. Low-energy studies. Phys Rev 110(1):185–203

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38. Dytman SA and Meyer AS (2011) Final state interactions in GENIE. In: AIP Conference Proceedings, vol 1405, p 213 39. Ashery D, Navon I, Azuelos G, Walter HK, Pfeiffer HJ, Schlepütz FW (1981) True absorption and scattering of pions on nuclei. Phys Rev C 23(5):2173–2185 40. Andreopoulos C et al (2015) The GENIE neutrino Monte Carlo generator: physics and user manual. arXiv: 1510.05494 [hep-ph] 41. Salcedo L, Oset E, Vicente-Vacas M, Garcia-Recio C (1988) Computer simulation of inclusive pion nuclear reactions. Nucl Phys A 484(3):557–592 42. Antonello M et al (2015) A proposal for a three detector short-baseline neutrino oscillation program in the fermilab booster neutrino beam. arXiv: 1503.01520 [physics.ins-det] 43. Habig A (2012) The NOvA experiment. Nucl Phys B-Proc Suppl 229–232:460; Neutrino 2010 44. Abe K et al (2011) The T2K experiment. Nucl Instrum Methods Phys Res Sect A: Accel Spectrometers Detect Assoc Equip 659(1):106–135 45. Abe et al K (2018) Hyper-Kamiokande design report. arXiv:1805.04163 [physics.ins-det] 46. Nikolakopoulos A, Jachowicz N, Van Dessel N, Niewczas K, González-Jiménez R, Udías JM, Pandey V (2019) Electron versus muon neutrino induced cross sections in charged current quasielastic processes. Phys Rev Lett 123(5) 47. Eichten T et al (1973) High energy electronic neutrino (ve) and antineutrino (ve) interactions. Phys Lett B 46(2):281–284 48. Blietschau J et al (1978) Total cross sections for νe and ν¯ e interactions and search for neutrino oscillations and decay. Nucl Phys B 133(2):205–219 49. Assylbekov S et al (2012) The T2K ND280 off-axis pi-zero detector. Nucl Instrum Methods Phys Res Sect A: Accel Spectrometers Detect Assoc Equip 686:48–63 50. Abe K et al (2014) Measurement of the inclusive electron neutrino charged current cross section on carbon with the T2K near detector. Phys Rev Lett 113(24):241803 51. Abe K et al (2015) Measurement of the electron neutrino charged-current interaction rate on water with the T2K ND280 π0 detector. Phys Rev D 91(11):112010 52. Abe K et al (2020) (2020) Measurement of the charged-current electron (anti-)neutrino inclusive cross-sections at the T2K off-axis near detector ND280. J High Energy Phys 10:114 53. Wolcott J et al (2016) Measurement of Electron Neutrino Quasielastic and Quasielasticlike Scattering on Hydrocarbon at E ν  = 3.6 GeV. Phys Rev Lett 116(8):081802 54. Acciarri R et al (2020) First measurement of electron neutrino scattering cross section on argon. Phys Rev D 102(1):011101

Chapter 4

MicroBooNE as a LArTPC Detector

The liquid argon time projection chamber (LArTPC) is a technology that detects the ionisation and scintillation signals produced by charged particles in its volume. These detectors are capable of obtaining excellent calorimetry and spatial resolutions down to the scale of millimetres. The Micro Booster Neutrino Experiment (MicroBooNE) uses the LArTPC technology and is located on-axis to the Booster Neutrino Beamline (BNB) 470 m downstream of the neutrino target and off-axis to the Neutrinos at the Main Injector (NuMI) beam. This chapter firstly covers physics principles of LArTPCs followed by how they are implemented in MicroBooNE which was used to acquire the data used in this thesis.

4.1 Liquid Argon Time Projection Chambers The LArTPC consists of a large volume of liquid argon. Charged particles produced inside, or that enter the detector, ionise the argon along their path. A uniform electric field drifts the ionisation charge towards the anode where the signal is recorded by a set of wire planes. Scintillation light is also produced inside the detector from the excitation and ionisation of the argon caused by the charged particles. This light is collected by photomultiplier tubes (PMTs) located behind the anode providing prompt information about the neutrino interaction time. An example diagram of a LArTPC is shown in Fig. 4.1. The properties of the noble element argon make it ideal for use in a TPC. It is chemically inert which allows the ionisation electrons to drift large distances (∼m) without being absorbed. It is relatively cheap, readily available, stable and has a relatively low mean ionisation potential (23.6 eV). In addition, the high density of argon allows for a compact detector with a good event rate compared with lighter mediums such as water. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 K. V. J. Mistry, Exploring Electron-Neutrino–Argon Interactions, Springer Theses, https://doi.org/10.1007/978-3-031-19572-3_4

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4 MicroBooNE as a LArTPC Detector

Fig. 4.1 A diagram of a LArTPC. The charged daughter particles produced from the neutrino interaction ionise and excite the argon. An electric drift field is applied which drifts these ionisation electrons to a set of wire planes where the signal is recorded. These wire planes are oriented at different angles to produce an image of the interaction in different projections. Figure from Ref. [1] c 2017 IOP Publishing, reproduced with permission, all rights reserved 

4.2 Particle Interactions with Argon LArTPCs can only detect charged particles which ionise or excite the argon and are not able to detect any neutral particles such as neutrinos, neutrons or photons directly. However, they can detect the latter indirectly by observing any charged particles which are produced from interactions of these particles with the argon. Common particles produced in a neutrino interaction include: muons, electrons, protons, charged and neutral pions, neutrons and photons. This section discusses the interactions of these particles with matter and what signature they produce in a LArTPC.

4.2.1 Charged Particle Energy Loss Charged particles that traverse the liquid argon medium ionise the argon depositing small amounts of energy along their trajectory by Coulomb scattering with atomic

4.2 Particle Interactions with Argon

35

electrons. The mean energy loss per unit distance travelled can be described by the Bethe-Bloch formula which is given by: 

     2 2 2 2 dE δ(βγ) 2m e c β γ Wmax 2Z 1 1 2 −β − = Kz , − ln dx A β2 2 I2 2

(4.1)

where x is the distance through the medium, β = v/c, γ = (1 − β 2 )−1/2 , Wmax is the maximum possible energy transfer of a collision, δ(βγ) is a term to account for the effect of the density of the medium on the energy loss, I is the mean ionisation potential of the atoms averaged over all electrons, Z is the atomic number of the medium, z is the charge of the incident particle, A is the atomic mass of the medium and K = 4π N A re2 m e c2 where N A is Avogadro’s number, re is the classical electron radius, and m e c2 is the electron rest mass energy [2]. There are some important features of the energy loss of a charged particle in a medium: • The energy loss rises rapidly at low β i.e. as the particle slows down its energy loss rises very steeply. • The energy loss reaches a minimum for all particles in the range of βγ ∼ 3 − 4. These particles are called Minimum Ionising Particles (MIPs). • Beyond the MIP region, β tends to one and the logarithmic factor “kicks in” resulting in a relativistic rise in the energy loss and then flattens off due to the δ term which characterises shielding in a dense medium. • The energy loss magnitude depends on the medium. • The Bethe-Bloch formula describes the mean energy loss. The distribution of the energy loss is a stochastic process and its values at a given point are distributed with a Landau distribution. Figure 4.2 shows the energy loss for muons, pions and protons in several mediums. For neutrino interactions in MicroBooNE, the relevant energy range of the observed particles is a few hundred MeV to a few GeV. The energy loss is heavily dependent on the mass of the particle. Protons produced from neutrino interactions are likely to be created in the steep rising region of the Bethe-Bloch curve where they exhibit a high d E/d x. Muons and pions are likely to be produced in the MIP region which is around 2.2 MeV/cm in argon. As a particle deposits energy it moves towards the low-energy rise in the Bethe-Bloch curve. In this region, its deceleration increases and the particle comes to an abrupt stop depositing a large amount of energy at the end of its trajectory. This characteristic signature is usually called the Bragg peak. In some cases (in the high energy tail of the Landau distribution), large energy transfers can kick out an electron with enough energy to produce further ionisation. These electrons are known as δ-rays. For electrons and positrons at low energies (below a few tens of MeV) where ionisation losses by collisions are important, the mean energy loss is slightly different compared to heavier particles such as protons, muons and pions. This is because there can be large transfers of energy with the atomic electrons in the medium which are described by Møller scattering for electrons and Bhabha scattering for positrons. The

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4 MicroBooNE as a LArTPC Detector

Fig. 4.2 The Bethe-Bloch curve showing energy loss as a function of momentum for a few selected elements. The primary x-axis shows the βγ value while the axes below this show the corresponding momentum for different particle types. Figure from Ref. [2], licensed under CC-BY-4.0

difference in these scattering mechanisms also leads to a tiny difference in the energy loss between these particles due to the additional contribution from annihilation in Bhabha scattering. The amount of ionisation depends on the momentum transfer of these collisions. Figure 4.3 shows the energy loss of electrons and positrons in argon as a function of the kinetic energy [2, 3].

4.2.2 Chargeless Particle Interactions Neutral particles emitted from the interaction of a neutrino with argon commonly include neutrons, π 0 and γ. Neutrons can elastically/inelastically scatter or get captured on an argon nucleus. However, in the energy range from a few hundred MeV to a few GeV, elastic/inelastic scattering dominates. As a result, neutrons are largely undetectable in a LArTPC since the small energy depositions from the elastic/inelas-

4.2 Particle Interactions with Argon

37

Fig. 4.3 (left) The energy loss of electrons on argon broken down by the contributions from collision (blue) and radiation (red) losses. (right) The energy loss of electrons and positrons on argon. The blue and red lines are taken from the ICRU report number 37 [4] and have no density corrections applied. The green line is from using NIST ESTAR tabulated data [5], the magenta line c 2020 is obtained by applying the Bethe-Bloch energy loss to electrons. Figures from Ref. [3]  IOP Publishing, reproduced with permission, all rights reserved

tic scatters are challenging to reconstruct. In the case of π 0 , the dominant channel is a prompt decay into two photons. Photons are also neutral, but can be detected via their main interaction modes. These are shown as a function of energy for lead as an example in Fig. 4.4. For photons at energies above 100 MeV, the dominant mechanism of interaction is via pair production. At lower energies, Compton scattering effects become important contributions up to energies of ∼1 MeV where the photoelectric effect becomes the most important contribution.

4.2.3 Electromagnetic Showers Electromagnetic (EM) showers are a cascade of secondary particles induced in a medium consisting of dense matter by a high energy >100 MeV electron or photon. The main dominant channel of energy loss for electrons at these energies is by radiation as shown in Fig. 4.3. For photons, the interactions at these energies are dominated by pair production. As shown in Fig. 4.5, this process continues creating a cascade of particles until radiation losses equal those from ionisation/excitation which happens at the critical energy, E c . The scale of EM showers are characterised by the radiation length, X 0 , which is the mean distance for which an electron (or photon) loses all but 1/e of its energy by bremsstrahlung (or pair production). The value of X 0 in argon is 14 cm [2]. The transverse profile of an EM shower is characterised by the Molière radius, R M , which is the radius of a cylinder that contains 90% of the initial energy of the

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4 MicroBooNE as a LArTPC Detector

Fig. 4.4 The cross section of photon interactions with lead as a function of energy. The cross section is broken down by the various modes of interactions with contributions from a the photoelectric effect, b Rayleigh scattering, c Compton scattering, d pair production in the field of a nucleus and e pair production in the field of atomic electrons. Figure from Ref. [2], original figure through the courtesy of John H. Hubbell (NIST)

Fig. 4.5 The development of an EM shower initiated by (left) electron/positrons and (right) photons. One of the key ways to separate these particle cascades is to analyse the energy loss at the start of the shower. In the case of electrons, the energy loss is given by a single MIP particle whereas for photons it is given by two MIP particles

EM shower. This effective transverse containment arises because bremsstrahlung and pair production processes have small opening angles. The Molière radius is related to the radiation length by the equation, RM =

Es X 0, Ec

(4.2)

4.3 LArTPC Detector Effects

39

√ where E s = m e c2 4π/α  21.2 MeV is the scale energy and α is the fine structure constant [2].

4.3 LArTPC Detector Effects Following a neutrino interaction, charged particles leave a trail of ionisation along their path. There are approximately 105 electrons produced per MeV deposited and due to the low electronegativity of argon, this allows the ionisation electrons or “clouds” to drift under the electric field applied towards the wire planes at the anode. Several processes can affect the ionisation clouds. This includes diffusion, distortions in the electric field due to Ar+ ions, impurities in the argon, and electron-ion recombination whereby the ionisation electrons re-combine with argon ions and create scintillation photons.

4.3.1 Diffusion As the clouds of electrons originating from ionisation drift towards the anode1 the distributions can spread out. This spreading out is non-isotropic because of the presence of the electric field and is characterised by two components: perpendicular to the drift direction (transverse diffusion) and parallel to the drift direction (longitudinal diffusion). Ionisation clouds which originate near the cathode are most affected by the effects of diffusion because they have to travel the full drift length of the TPC. The effects of longitudinal diffusion on the waveforms recorded on a wire are shown in Fig. 4.6 as a function of drift time. The width of a signal pulse, σ(t) after drifting a time, t, is given by, σ 2 (t) = 2Dt,

(4.3)

where vd is the drift velocity and D is the diffusion constant. The diffusion constant is given by the classically-derived Nernst-Townsend formula, D=

μ , e

(4.4)

where μ is the electron mobility, e is the electron charge and  is the electron energy [7].

1

The average drift velocity is vd = 1.076 mm/µs at an electric field of 273.9 V/cm [6].

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4 MicroBooNE as a LArTPC Detector

Fig. 4.6 The effect of longitudinal diffusion on the charge waveform recorded at the wires. The different slices show the effect of longitudinal diffusion for increasing drift time which further broadens the charge width and reduces in size. Figure from Ref. [6], licensed under CC-BY-4.0

4.3.2 Space Charge Effect Ionisation in the detector creates Ar+ ions which drift at a rate much slower than ionisation electrons. For detectors on the surface, a large number of cosmic ray interactions can be expected. As a result, Ar+ ions can build up, mainly towards the cathode, distorting the electric field uniformity in the detector. This is known as the space charge effect (SCE). As ionisation clouds drift toward the wire planes, the nonuniform electric field can distort the trajectories of the electrons affecting the observed interaction topologies. Figure 4.7 shows the effect of the SCE on reconstructed cosmic muon tracks. The build-up of ions is most significant near the cathode of the detector where the majority of Ar+ ions are located at given time.

4.3.3 Electron-Ion Recombination Electron-ion recombination describes the process where ionisation electrons thermalise by interacting with the surrounding medium and recombine with nearby Ar+ ions instead of being drifted away by the electric field. The dominant form of recombination in a LArTPC is described under a columnar model [9] which depends on the collective electron and ion charge density from multiple ionisations within a cylindrical volume. Assuming a Gaussian spatial distribution around the particle trajectory and “Box model” boundary conditions (which assume diffusion and ion mobility

4.3 LArTPC Detector Effects

41

Fig. 4.7 Entry/exit points (in blue) of reconstructed muon tracks inside the MicroBooNE detector in the x − y plane which have been distorted from the space charge effect. In this plot, x is in the drift direction with the cathode located at x ∼ 250 cm and y is from bottom to top of the TPC. In the absence of the space charge effect, the reconstructed points should lie at the TPC boundaries c 2020 IOP Publishing, reproduced with permission, all rights (dashed lines). Figure from Ref. [8]  reserved

are negligible), the fraction of ionisation electrons that survive recombination, R, is given by: 1 ln(α + β (d E/d x)), (4.5) R= β (d E/d x) where α is a recombination coefficient and β is a free parameter that incorporates information about the electric field strength. Reconstruction of the d E/d x of a particle track can then be found by the relation, d E/d x = (d Q/d x)/RWion ,

(4.6)

where Wion = 23.6 eV is the energy required to ionise an argon atom. The values of α and β can be tuned to values that match data from an experiment. This tuned Box model is known as the “Modified Box” model [10].

4.3.4 Argon Purity While ionisation electrons can drift large distances in liquid argon, impurities with a high electronegativity within the argon can capture these electrons before they reach the wire planes. The most significant impurities include water and oxygen. The electron drift lifetime is inversely proportional to the impurity concentration in the liquid argon and on the electric field strength. Oxygen contamination of up to 50 parts per trillion at an electric field of 273.9 V/cm and a drift distance of 250 cm

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4 MicroBooNE as a LArTPC Detector

can lead to an attenuation of the signal by up to 32% [11]. Because such a small contamination of impurities can cause a significant effect on the performance of the detector, the purity in a LArTPC needs to be monitored daily.

4.4 LArTPC Scintillation Light 4.4.1 Scintillation Light Production Scintillation light is produced in liquid argon due to ionisation and excitation of charged particles passing through it. As shown in Fig. 4.8, this light is emitted after the deexcitation of two distinct excimer states, singlet and triplet, which are formed via two processes: • Self-trapped exciton luminescence: Charged particles excite the argon. These excited states then form the singlet state in 65% of cases and triplet in 35% of cases. • Electron-ion recombination: Charged particles ionise the argon. These ionisation electrons can recombine with the argon to form the singlet and triplet excimer states in equal proportion. The lifetimes of the excimer states have two distinct values described by an exponential decay function. The singlet state has a lifetime of ∼6 ns and gives rise to

Fig. 4.8 A flow chart showing the channels leading to scintillation light in liquid argon. In the top channel, charged particles excite the argon leading to self-trapped exciton luminescence. In the bottom channels, charged particles ionise the argon leading to recombination. Both channels form excimer states which give rise to the scintillation. Impurities can quench or absorb these excimer states so LArTPC’s require high purities to maintain sufficient light yields. Figure from Ref. [12], licensed under CC-BY-4.0

4.5 MicroBooNE TPC

43

the fast component of the scintillation light. The triplet state has a longer lifetime of ∼1.6 µs giving rise to a slower component. The wavelength of scintillation light is in the vacuum ultraviolet (VUV) range at 128 nm. The yield of light depends on a number of factors including the ionising particle type, electric field strength in the detector and purity of liquid argon. For the electric field strengths of 500 V/cm about 24,000 photons are emitted per MeV of deposited energy [1].

4.4.2 Scattering and Attenuation An important aspect of the scintillation light from argon is that the argon is transparent to the VUV wavelength scintillation light. [13]. With an energy of 9.7 eV, VUV scintillation photons have a high probability of undergoing Rayleigh scattering. This type of interaction is where a photon scatters elastically and coherently with a nucleus. The photon does not lose any energy, but does change direction. As shown in Fig. 4.8, impurities can attenuate the amount of scintillation light by quenching and absorption. Common impurities inside a LArTPC that can cause this are nitrogen, oxygen and water.

4.5 MicroBooNE TPC The MicroBooNE TPC is housed inside a cylindrical cryostat containing a total mass of 170 tonnes of liquid argon. The structure inside the cryostat consists of three main pieces: the cathode, field cage and anode. The active volume of the TPC, defined by the TPC field cage, is a rectangular cuboid that has dimensions of 2.6 m (width) × 2.3 m (height) × 10.4 m (length). The MicroBooNE TPC has three wire planes located at the anode. The wires are made from stainless steel (diameter 150 µm) coated with a thin layer of copper (2 µm) and silver (0.1 µm). The first two planes (referred to as the “U” and “V” induction planes) have 2400 wires which are oriented at ±60◦ with respect to the vertical. The final wire plane, known as the “Y” or collection plane, is oriented vertically and consists of 3456 wires. The spacing between each wire is 3 mm. A voltage of −70 kV is applied to the cathode and a uniform electric field is created inside the detector to the anode using a series of field rings connected by a voltage divider chain. MicroBooNE operates with an electric field of 273.9 V/cm which results in a drift time from cathode to anode of 2.3 ms. This is the time that defines a single readout frame in MicroBooNE. The argon is operated with a temperature of 89 K and pressure of 1.24 bar. A total of 32 PMTs are housed behind the wire planes to detect the scintillation light produced in the detector. Figure 4.9 shows a schematic of the MicroBooNE TPC.

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Fig. 4.9 A schematic of the MicroBooNE TPC. The cryostat is cylindrical in shape and houses c 2017 IOP Publishing, reproduced with the active volume of the TPC. Figure from Ref. [1]  permission, all rights reserved

The MicroBooNE detector is subject to a large flux of cosmic rays passing through it because it is located on the surface. Within a given 2.3 ms readout frame, there can be as many as 20–30 cosmic ray muons.

4.5.1 MicroBooNE Charge Collection MicroBooNE has three wire planes. The first two induction planes are biased with voltages of −110 V (U plane) and 0 V (V plane) such that the drift electrons pass through the wire planes which induces a bi-polar signal on the wires. The final plane is biased at 230 V such that the drift electrons are collected producing a unipolar signal. The shapes of these signals in each of these planes are shown in Fig. 4.10. Signals from the wires are sampled with a frequency 2 MHz, this defines one time “tick” as 0.5 µs of drift time. Signals are read out by cryogenic low-noise front end Application Specific Integrated Circuits (ASICs) which pre-amplify and shape the signal before sending them to the front end readout modules outside the TPC. These modules digitise the signals and send them to the data acquisition system (DAQ) to convert signals from an analog to digital format and save the information.

4.5 MicroBooNE TPC

45

Fig. 4.10 The charge signals recorded on the U, V and Y planes in MicroBooNE. The first two induction planes (U and V) have a bipolar signal due to the charge being induced in these wires. The Y plane has a unipolar signal due to the charge being collected in these wires. Figure from c 2018 IOP Publishing, reproduced with permission, all rights reserved Ref. [14] 

4.5.2 MicroBooNE Light Collection System The MicroBooNE PMT system consists of 32 8-inch Hamamatsu R5912-02mod PMTs. These PMTs are suitable for cryogenic temperatures and are located behind the wire planes at the anode. Figure 4.11 shows an image of this system installed in the MicroBooNE cryostat along with a diagram of the PMT. These PMTs can detect photons with wavelengths above (300–650) nm with a maximum quantum efficiency of 20% at ∼400 nm. Given the wavelength of the VUV scintillation light is 128 nm, a plate coated with tetraphenyl-butadiene (TPB) is placed in front of the PMT photocathode which absorbs the VUV light and re-emits it with a wavelength of 425 ± 20 nm, a region where the PMTs are sensitive. Signals at each PMT are digitised at a rate of 64 MHz using an analog-to-digital (ADC) converter. Recording the scintillation light in MicroBooNE serves as an important tool for identifying the time of the interaction since the photons are released promptly. In addition, the intensity of the light is used as part of the trigger system and in the reconstruction to identify neutrinos.

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4 MicroBooNE as a LArTPC Detector

Fig. 4.11 (left) A diagram of the PMT used in the MicroBooNE detector and (right) an image of c 2017 the MicroBooNE PMTs installed inside the cryostat of the detector. Figure from Ref. [1]  IOP Publishing, reproduced with permission, all rights reserved

4.6 MicroBooNE Readout and Trigger System 4.6.1 MicroBooNE Readout A MicroBooNE event consists of two parts, a continuous readout of 6.4 ms of the PMT system and a continuous readout of 4.8 ms of the TPC system. For the TPC readout, frames are read out in 1.6 ms sizes. This frame size was designed for MicroBooNE’s operating field of 500 V/cm. At the operating field of 273.9 V/cm, the drift time for electrons is 2.3 ms. To ensure the neutrino is properly read out, a total of three TPC readout windows (giving a total of 4.8 ms) are opened with one frame before the expected neutrino interaction, and two frames after.2 See Fig. 4.12 for a visual representation of an event readout. During the readout for the PMT system, to reduce the amount of data recorded, only PMT waveforms (≥9.5 photo-electrons(PE)) for about 40 samples or 0.6 µs are saved. A dead-time of 45 samples is additionally included after each PMT waveform is saved. An event is only read out following a trigger signal. The various triggers used in MicroBooNE are described in the following sections.

4.6.2 Beam Hardware Trigger The neutrino beam is run by the Fermilab Accelerator Division (AD) which informs MicroBooNE when protons are collided on a target to produce neutrinos (known as a “spill”). This signal is known as the hardware trigger (HW trigger). It is used to start the readout of an unbiased (no light intensity requirements) window lasting 2

In the special case a cosmic ray crosses the anode and cathode of the detector (2.3–1.6) ms before the HW trigger (or a similar trajectory), due to the readout frame size of 1.6 ms, a portion of the cosmic ray energy depositions in the detector will be truncated due to the 2.3 ms drift time.

4.6 MicroBooNE Readout and Trigger System

47

Fig. 4.12 A schematic of the various terms in the MicroBooNE readout and trigger system. The HW trigger signal sent from the Fermilab accelerator division starts the readout of the event which is 6.4 ms for the PMT system and 4.8 ms for the TPC readout. Following the HW trigger, an unbiased window of 23.4 µs is opened where the beam spill is located. A slightly wider SW trigger window is used around the NuMI spill window. In the case of the external trigger, a pulser is used instead of the beam HW trigger

23.4 µs, called the “beamgate window”, starting 1.6 ms into the TPC readout frame. With respect to the start of the beamgate window, the NuMI beam spill time window ranges from 5.64 µs and 15.44 µs.

4.6.3 Software Trigger Due to the small neutrino cross section, only 2–3% of the spills from the NuMI beam result in a neutrino interaction in MicroBooNE. By triggering on every spill, many of the HW triggers will not contain a neutrino interaction. To avoid recording a significant number of these empty events, they are first stored in a buffer where they are filtered by a second trigger stream, the software trigger (SW trigger). The SW trigger requires the event to have a minimum scintillation light amount of ≥9.5 PE inside the beamgate window from (4.69–16.41) µs to keep the event. Events passing the SW trigger are recorded to tape storage for analysis. The passing fraction of events from the SW trigger is ∼14% of all HW triggers.

4.6.4 External and Unbiased Trigger Many of the MicroBooNE spills recorded do not contain a neutrino interaction. However, these events may have cosmic rays passing through the detector that produce

48

4 MicroBooNE as a LArTPC Detector

enough light in the SW trigger window to satisfy the trigger threshold. To model these type of interactions, MicroBooNE has a configurable pulse generator which is used to trigger the readout of events explicitly when there is no beam. These random events that also pass the SW trigger are then classified as external events. Additionally, a fraction of these events that do not pass the SW trigger are also recorded. These are known as unbiased events and contain data recorded cosmic rays without any requirements on the timing and light intensity.

4.7 MicroBooNE Event Display A LArTPC such as MicroBooNE is capable of producing photographic quality images of neutrino interactions. To demonstrate this, an example event display from the MicroBooNE detector recorded from each wire plane in MicroBooNE is shown in Fig. 4.13. These displays are created from the charge deposited on each wire plane where each plane provides a different angular perspective of an interaction. The colour scale is proportional to the charge deposited, where high ionisation is shown

Fig. 4.13 Event display recorded from the MicroBooNE detector for a candidate electron neutrino from the NuMI beam for the (top left) collection, (top right) V and (bottom) U planes. The U plane provides the best view of the additional two showers displaced from the vertex of the interaction which have likely come from the decay of a π 0 → γγ

References

49

in red and low ionisation in green. The collection plane view is equivalent to looking top down on the interaction, where the V and U planes are looking at the interaction at a ±60◦ angle. The excellent resolution of the detector allows many fine details of the neutrino interaction to be resolved.

References 1. Acciarri R et al (2017) Design and construction of the MicroBooNE detector. J Instrum 12(02):P02017 2. Zyla P et al (2020) Review of particle physics. PTEP 2020(8):083C01; and 2021 update 3. Abratenko P et al (2020) Reconstruction and Measurement of O(100) MeV Energy Electromagnetic Activity from π 0 → γγ Decays in the MicroBooNE LArTPC. J Instrum 15(2):P02007 4. I. R. 37 (1984) Stopping powers for electrons and positrons, international commission on radiation units and measurements 5. Berger M et al Xcom: Photon cross section database (version 1.5). https://physics.nist.gov/ PhysRefData/Star/Text/method.html, Date of information accessed: 2017, 2010 6. Abratenko P et al (2021) Measurement of the longitudinal diffusion of ionization electrons in the MicroBooNE detector. J Instrum 16(09):P09025 7. Sauli F (2014) Gaseous radiation detectors: fundamentals and applications. Nuclear physics and cosmology. Cambridge monographs on particle physics. Cambridge University Press 8. Abratenko P et al (2020) Measurement of space charge effects in the Micro- BooNE LArTPC using cosmic muons. J Instrum 15(12):P12037 9. Jaffé G (1913) Zur theorie der ionisation in kolonnen. Ann Phys 347(12):303–344 10. Acciarri R others (2013) A study of electron recombination using highly ionizing particles in the ArgoNeuT Liquid Argon TPC. J Instrum 8(08):P08005 11. The MicroBooNE Collaboration (2016) Measurement of the electronegative contaminants and drift electron lifetime in the MicroBooNE experiment. MicroBooNE Public Note No. 1003 12. Van De Pontseele W (2020) Search for electron neutrino anomalies with the MicroBooNE Detector. FERMILAB-THESIS-2020-11, Ph.D. dissertation, Oxford University Press 13. Mulliken RS (1970) Potential curves of diatomic rare? Gas molecules and their ions, with particular reference to Xe2. J Chem Phys 52:5170–5180 14. Adams C et al (2018) Ionization electron signal processing in single phase LArTPCs. Part II. Data/simulation comparison and performance in MicroBooNE. J Instrum 13(07):P07007

Chapter 5

The NuMI Beam and Neutrino Flux Prediction at MicroBooNE

The NuMI beam is a neutrino beam located at Fermilab, Chicago originally built for the MINOS long-baseline oscillation experiment. To the present day, NuMI has provided beam to a number of experiments including MINOS(+)[1], MINERvA [2], ArgoNeuT [3] and NOvA [4]. While MicroBooNE is primarily designed to receive neutrinos from the BNB, it also receives a significant flux of neutrinos from NuMI. This positioning allows MicroBooNE to make measurements using two independent neutrino beams, with the NuMI beam being utilised for cross section measurements, beyond the standard model searches and validation of electron neutrino reconstruction at low energies. This chapter describes the determination and validation of the NuMI neutrino flux prediction at MicroBooNE.

5.1 Neutrino Production Figure 5.1 shows a diagram outlining the components of the accelerator complex at Fermilab relevant to the creation of the NuMI neutrino beam. To create the beam, protons are created by accelerating H− ions to 400 MeV using a linear accelerator (Linac). The ions are stripped of two electrons and converted to protons after passing by a carbon foil. The protons are then sent to the Booster synchrotron where they are accelerated to 8 GeV. The protons at this stage can either be steered to collide with a beryllium target to make the BNB beam or sent towards the Main Injector, a synchrotron which further accelerates the protons to 120 GeV. The NuMI beam is then created by steering these protons to collide with a graphite target. Following the collision of protons with the NuMI graphite target, a cascade of particles is produced as shown in Fig. 5.2. These particles include pions, and kaons which are focussed using two magnetic van der Meer horns. In the case of a positive horn current applied to the horns, known as Forward Horn Current (FHC) mode, © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 K. V. J. Mistry, Exploring Electron-Neutrino–Argon Interactions, Springer Theses, https://doi.org/10.1007/978-3-031-19572-3_5

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5 The NuMI Beam and Neutrino Flux Prediction at MicroBooNE

Fig. 5.1 Diagram showing the Linac, Booster synchrotron and Main Injector as well as the directions of the NuMI and BNB beams with respect to MicroBooNE

Fig. 5.2 A simplified diagram of the NuMI neutrino beamline. Neutrinos are created by colliding protons with a graphite target producing a cascade of particles including pions, kaons and muons. Particles of a particular electric charge are focused by two magnetic focussing horns. After being focussed, the particles travel down a 675 m long decay pipe to decay. The absorber attenuates any remaining hadrons and muons in the beamline leaving a beam of neutrinos beyond this. Note, the location of the target in this diagram is exaggerated. In reality, it is located partially into the first horn

positively charged particles are focussed in the beamline direction. For a negative horn current applied to the horns, known as Reverse Horn Current (RHC) mode, negatively charged particles are focussed. Following this, the charge selected particles1 travel down a 675 m decay pipe filled with helium2 where they decay to

1

Note that the horns are not 100% perfect at selecting a specific electric charge so there can be contamination of “wrong sign” particles in the neutrino beam. 2 The helium was introduced in 2007 to reduce corrosion in the pipe.

5.2 The NuMI Beam

53

neutrinos. The particles that travel the length of the decay pipe3 are terminated at a large structure consisting of aluminium, steel and concrete known as the absorber. Beyond this point, there is a “muon-shield” consisting of dolomite rock lasting for more than 200 m. This leaves a beam of predominantly muon neutrinos travelling in the forward direction of the beamline [5].

5.2 The NuMI Beam The NuMI beam started running in 2005 and over its lifetime it has operated in a few different energy configurations. These configurations can generally be split into two eras: the Low Energy (LE) (2005–2012) and Medium Energy (ME) (2012—present) eras. The different energy regimes are configured by changing the separation, the magnitude and the polarity of the magnetic fields for the horns, and the position of the target. The tunable energy beam allows oscillation experiments in the NuMI beamline to study a range of neutrino oscillation parameters [5]. For the duration of the MicroBooNE data taking, NuMI operated in the ME configuration. In this configuration, the second magnetic horn is moved downstream relative to the first horn and the target position is moved upstream. Examples of the LE and ME fluxes for MINERvA and the off-axis NOvA near detector are shown in Fig. 5.3 [6].

Fig. 5.3 The fluxes for the MINERvA and the NOvA near detector in the ME NuMI configuration. In addition, the LE configuration flux is shown for MINERvA. Figure from Ref. [6], licensed under CC-BY-4.0

3

About 80% of these particles are protons in the initial beam that did not interact and travelled the length of the decay pipe.

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5 The NuMI Beam and Neutrino Flux Prediction at MicroBooNE

5.2.1 Neutrino and Antineutrino Modes The NuMI beam can operate in two neutrino modes based on the polarity of the magnetic focussing horns, passing +200 kA of current for FHC mode and −200 kA for RHC mode. The polarity can either enhance the content of either νe and νμ (FHC) or ν¯ e and ν¯ μ (RHC) for on-axis or close to on-axis experiments. The dates the NuMI beam operated in each of these modes since 2014 is reported in Fig. 5.4 which shows the cumulative total protons on target (POT) delivered by the NuMI beam. For reference, Table 5.1 outlines the dates the NuMI beam was in FHC or RHC mode during the MicroBooNE run periods. This thesis focuses only on the FHC data collected during the Run 1 period for MicroBooNE (23 October 2015–2 May 2016).

Fig. 5.4 The total cumulative POT delivered by the NuMI beamline. The orange regions labelled neutrino mode refer to the FHC mode of operation, whilst the blue highlighted regions correspond to the RHC mode. The regions where there was no POT delivered are due to periods where the accelerator complex is shut down for maintenance periods. MicroBooNE Run 1 FHC is the run period relevant to this thesis. Figure adapted from Ref. [7] Table 5.1 Table showing the dates and mode of operation of the NuMI beam during the MicroBooNE run periods. This thesis focuses only on the FHC data collected during the Run 1 period Run Period

FHC (+200 kA)

Run 1 Run 2

23 October 2015 - 2 May 2016 29 June 2016–29 July 2016 14 Nov 2016 - 20 Feb 2017 11 Nov 2016–14 Nov 2017 20 Feb 2017–7 July 2017 N/A 7 Nov 2017–6 July 2018 26 Feb 2019–6 July 2019 20 Oct 2018–26 Feb 2019 29 Oct 2019–20 March 2020 N/A

Run 3 Run 4 Run 5

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5.2 The NuMI Beam

55

5.2.2 NuMI Protons: Timing, Slip-Stacking and Intensity In the Fermilab accelerator complex, proton batches coming from the Booster synchrotron feed into the Main Injector where they are further accelerated, extracted and directed to the NuMI target. Each Booster batch is 1.6 μs long and it is subdivided into 84 buckets with 53 MHz spacing. A total of 81 of these buckets are occupied with protons forming proton “bunches”. The total number of protons delivered per batch is approximately 5.0 ×1012 POT. This is the same number of protons delivered in a BNB spill which consists of a single batch. Since the Main Injector has a proton storage capacity seven times larger than the Booster, it stores and accelerates six Booster batches with one slot left empty to allow time for the extraction kicker magnets to ramp up. The six batches form a 9.6 µs “spill” that determines the timing structure of the NuMI beam. Figure 5.5 shows a pictorial diagram of the “spill”,“bunch” and “batch” terminology. The proton intensity in NuMI is enhanced through slip-stacking—the process of combining two batches into one. Slip-stacking configurations are usually referred to in the form X+6 where X is the number of batches (out of 6) that have been combined. During MicroBooNE’s first period of data taking (Run 1), the NuMI beam was mostly set in the 4+6 configuration. NuMI began to transition to a 6+6 configuration in two stages in 2016 and stayed in this configuration throughout MicroBooNE’s remaining data taking period after this transition. Figure 5.6 shows the slip-stacking configurations used during the MicroBooNE Run 1 data period.

Fig. 5.5 A diagram showing the meaning of a bunch, batch and spill. Note that this diagram is not to scale so the spacing between the batches is smaller than the size of the bunches

5 The NuMI Beam and Neutrino Flux Prediction at MicroBooNE

Fig. 5.6 A stacked plot of the slip stacking configuration of the NuMI beam during Run 1 FHC data taking. In this case, the x-axis is the run number recorded by the MicroBooNE DAQ. These numbers are roughly proportional (with variance due to the stability of the DAQ) to the calendar time ranging from 23 October 2015–2 May 2016

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A NuMI spill corresponds to 3.0 × 1013 POT in the 0+6 configuration, 5.0 × 10 POT in the 4+6 configuration, 6.0 × 1013 POT in the 6+6 configuration. The increase in slip-stacking translates to an overall increase in integrated proton exposure as shown in Fig. 5.4 [5, 8]. In addition to slip-stacking, the spill repetition rate of the NuMI beam can be increased to boost the overall power of the beam. This can be done by using the Recycler4 to slip-stack while the Main Injector magnets ramp up. This results in a reduction in the cycle time from 2.2 s to 1.33 s. Figure 5.7 shows the total POT delivered as a function of run number split up by the 4+6 and 6+6 slip stacking periods. The POT delivered as a function of run number is constant across the 4+6 slip stacking periods; however, the two periods taken in 6+6 slip stacking modes have a different total POT delivered showing the beam repetition rate was increased in the second period of 6+6 slip stacking data [8]. 13

5.3 The NuMI Beam Simulation The simulation software of the NuMI beamline has been continually developed by a number of NuMI experiments. The software simulates the initial proton-target collision to the resulting hadrons and muons that decay to neutrinos using a beamline geometry that is modelled using GEANT4.5 This thesis uses two versions of the 4

The Recycler is a permanent magnet storage ring that shares the same tunnel as the Main Injector. It was originally designed to recycle antiprotons from the Tevatron. 5 GEANT4 version geant_4_2.p03 is used.

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Fig. 5.7 A diagram showing the total POT delivered as a function of run number split by the (left) 4+6 slip stacking and (right) 6+6 slip stacking periods in Run 1 FHC. While the 4+6 POT delivered is constant over time, the 6+6 slip stacking has a noticeable change in beam intensity. In this case, the x-axis is the run number recorded by the MicroBooNE DAQ. These numbers are roughly proportional to the calendar time ranging from 23 October 2015–2 May 2016

NuMI beam simulation that have different software and physics models to describe the hadron production, g4numi_flugg and g4numi. The g4numi_flugg is the first beamline simulation used in physics analyses in MicroBooNE with the NuMI beam. Because this simulation was not compatible with the software packages used to constrain the flux prediction, this simulation was updated to g4numi which is used in the differential cross section measurement in this thesis.

5.3.1 g4numi_flugg The g4numi_flugg simulation is one of the earliest simulations of the NuMI beam used by MINOS and further developed by NOvA. It uses a combination of the FLUKA software framework to model the hadron production and GEANT4 to handle the geometry of the beamline. The combination of these software packages is known as FLUGG.

5.3.2 g4numi The most up-to-date simulation of the NuMI beam uses g4numi which uses GEANT4 to model both the hadron production physics and beamline geometry. The physics model list use FTFP_BERT hadronic model which combines the FRITOF precompound model [9] for energies greater than 4 GeV and the Bertini cascade

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5 The NuMI Beam and Neutrino Flux Prediction at MicroBooNE

model [10] for energies less than 5 GeV. This model also incorporates the standard EM processes. This beamline simulation has now been adopted by all recent experiments using the NuMI beam including MINERvA, NOvA and MicroBooNE. The output files from this simulation are known as dk2nu files. Flux predictions made using this version of the beamline simulation in this thesis will be referred to as the g4numi flux simulation. This is also the primary beam simulation used in the extraction of the differential cross section presented in this thesis.

5.3.3 Beam Simulation Output The output files from the NuMI beam simulation store information about the ancestors that decay to neutrinos including the parent particle type, kinematics and decay position. Information such as the neutrino energy in the center of mass frame of the parent decay is also included. These files can be used to calculate the neutrino flux at any detector and volume, and as an input to a neutrino generator such as GENIE.

5.4 Flux Constraints with PPFX The Package to Predict the FluX (PPFX) is a package that implements constraints on the hadron production modelling and propagates uncertainties for the NuMI beamline simulation. It was written by L. Aliaga Soplin in the MINERvA collaboration and has now been adopted by other NuMI experiments including MINOS+ and NOvA [6]. The constraints use the information of the neutrino parentage from the output of the g4numi beamline simulation and are applied as a correction weight to each decay used in the generation of the flux prediction. PPFX includes two sets of data to constrain the flux prediction, thick and thin target data. This categorisation is based on the target size used by the experiments measuring hadron production. This thesis uses the thin target constraints option. This choice is motivated by the studies carried out by MINERvA which compared the agreement of the constrained flux prediction in each of these modes with an alternative in-situ method of calculating the flux. They find that the thin target constraints give a better agreement with the in-situ flux prediction [11]. The thin target data is from experiments using monochromatic beams on targets with a few interaction lengths. This data is generally published as invariant double differential cross sections as a function of the transverse momentum, pT , and Feynman-x scaling variable, x F , xF =

p||∗

2 p||∗ = √ , p||∗ (max) s

(5.1)

5.4 Flux Constraints with PPFX

59

where the ∗ indicates the rest frame of the √ hadron, p|| is the longitudinal momentum√of the produced particle and p||∗ (max)  s/2 is the maximum momentum allowed ( s is the centre of mass energy). The data is scaled using x F to incorporate measurements recorded with a different energy compared to the 120 GeV proton energy of NuMI. The thin target data implemented in PPFX includes: • Inelastic and Absorption Cross Sections – Belletini et al. [12], Denisov et al. [13]: proton, pions and kaons on many targets including carbon and aluminium in a wide energy range. – NA49: proton on carbon at 158 GeV [14]. – NA61: proton on carbon at 31 GeV [15]. • Hadron Production – – – – – –

Barton et al.: pC → π ± X at 100 GeV for x F > 0.3 [16]. NA49: pC → π ± X at 158 GeV for x F < 0.5 [17]. NA49: pC → n( p)X at 158 GeV for x F < 0.95 [18]. NA49: pC → K ± X at 158 GeV for x F < 0.2 [14]. NA61: pC → π ± at 31 GeV [15]. MIPP: pC → π ± X at 31 GeV [19].

PPFX uses this data where possible to apply corrections to a number of processes that affect the hadron production yields. Details of these corrections and their implementation from Ref. [6] are summarised here. Attenuation and Absorption Corrections Attenuation and absorption corrections account for the interactions of particles passing through the relevant components of the NuMI beamline such as the target, beam position monitors, horn inner conductors, decay pipe volume and decay pipe walls. These interactions depend on the cross section and the amount of material traversed. Weights are obtained from differences between data and MC on the survival/interaction probability of a particle with a material. Extending Data Coverage Using theoretical guidance, some datasets are extrapolated to different materials, and different incident and produced particles. One method involves a “material scaling” where data recorded on carbon is extrapolated to other materials. This is done using a parametrisation that depends on the ratio of the mass numbers of the nuclei and on a variable α(x F , pT ) which is determined from fits to data from Skubic et al. [20]. This data consists of invariant cross sections of protons interacting with various ¯ 0 . Additional uncertainties ranging from nuclei at 300 GeV producing K 0 , 0 and  (2.5–20)% depending on the particle type, pT and x F are assigned with this scaling approach.

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5 The NuMI Beam and Neutrino Flux Prediction at MicroBooNE

The isoscalar nature of 12 C can be used to infer that σ ( pC → π ± X ) = σ (nC → π X ). This symmetry is assumed for neutrons interacting with other materials. Additional uncertainties are not included with this assumption. Isospin symmetry in the quark-parton model [21] is assumed to apply corrections for neutral kaons based on interaction data from charged kaons. The correction is applied using the equation, ±

0 )= N (K L(S)

N (K + ) + 3N (K − ) . 4

(5.2)

No additional uncertainty is applied in this case because data uncertainties for charged kaon interactions are statistically dominated. Procedure Where there is no Applicable Data For uncertainties where there is no data coverage, data to model differences where there is data coverage are extrapolated to the uncovered regions. The reasoning for this extrapolation is motivated by the fact the hadronic model FTFP_BERT used in g4numi is a microphysical, first principles model of hadron production [6]. To apply corrections, data are categorised into four equal-sized regions in terms of x F (0–0.25, 0.25–0.5, 0.5–0.75 and 0.75–1.0) for any combination of incident and outgoing particle. An uncertainty of 40% is assigned in each of these regions and is treated as uncorrelated.

5.5 Neutrino Flux Calculation This section describes the steps needed to calculate the neutrino flux prediction at a detector. The flux calculation uses an analytical technique developed by Milburn [22] which was initially designed for the MINOS experiment in order to speed up the flux computation at the far detector. This method, however, can be generalised to any detector geometry and location. It works by replacing the initial Monte Carlo (MC) kinematics of the neutrino with an analytical calculation consisting of a rotation and Lorentz transformation of a solid angle in the rest frame of the decaying neutrino parent that points in the direction of the detector. Given that the neutrino parents are pseudoscalar, they decay with the neutrino emitted isotropically in their rest frame (exception for polarised muons). The output of this calculation is a weight that is applied to the decay to effectively give the probability of a decay resulting in a neutrino that goes through the detector. The following describes how this weight is calculated.

5.5 Neutrino Flux Calculation

61

Fig. 5.8 A diagram of the neutrino location weight. The solid angle subtended from the point picked in the detector is chosen to be on a circle with radius 100 cm

Location Weight (wloc ) For each decay, a point is randomly picked in detector volume and a circle of radius 100 cm is “drawn” as shown in Fig. 5.8. The probability that the neutrino will pass through the area of this circle is given by the solid angle subtended at this point (in the neutrino parent rest frame) divided by 4π . To incorporate this calculation into the flux, a weight (referred to as a “location” weight, wloc ) is derived which can be applied to each parent decay. The calculation of this weight is described in Ref. [22]. Area Weight (warea ) To obtain a flux in units per m2 , the flux is divided by the area of the circle used in the calculation of the location weight which is equal to π m2 . This is included as an additional weight, 1 warea = . (5.3) π Muon Polarisation Weight (wμ− pol ) To account for muon decays in flight where the muon is fully polarised from the decay of a pion it originated from, an additional weight is applied on top of the location weight. The distribution in the muon rest frame of νμ (¯νμ ) and νe (¯νe ) with energy E ν for the decay μ± → e± + νe (¯νe ) + ν¯ μ (νμ ) is given by the relation: d2 N 1 [ f 0 (x  ) ± Pμ f 1 (x  ) cos θ  ], = d x  d 4π

(5.4)

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5 The NuMI Beam and Neutrino Flux Prediction at MicroBooNE

Table 5.2 The flux functions in the muon rest frame calculated from the matrix elements of muon decay f 0 (x) f 1 (x) νμ , e νe

2x 2 (3 − 2x) 12x 2 (1 − x)

2x 2 (1 − 2x) 12x 2 (1 − x)

where x  = 2E ν /m μ , Pμ is the average muon polarisation along the beam direction (Pμ = +1 for νμ /νe and −1 for ν¯ μ /¯νe ) and  is the solid angle. The flux functions f 0 (x) and f 1 (x) are given in Table 5.2 [23]. Integrating Equation 5.4 over the solid angle we obtain, dN = f 0 (x  ). dx

(5.5)

The muon polarisation weight, wμ−pol , is then given by, wμ−pol = 4π

d2 N d x d2 N 1 = 4π , d N d x  d f 0 (x  ) d x  d

(5.6)

where the factor of 4π is introduced to cancel out the 4π steradian total solid angle assumed from an isotropic decay. For cases where the muon is captured or absorbed by a nucleus, the muon polarisation weight is not applied. Importance Weight (wimp ) To avoid overloading the beamline simulation files, certain decays with high statistics and in the same location are suppressed. This information is stored in the importance weight, wimp . For example, if there are enough cases of 200 MeV muon decays at the target, 1 out of 5 of these decays are stored with an importance weight equal to 5. PPFX weight (wppfx ) Using the hadron production constraints from PPFX on the output of the NuMI beamline simulation with external data, an additional correction factor, wppfx , is applied. Total Weight (wtot ) The total weight, wtot , is given by the product of each of these weights calculated, wtot = wloc × warea × wimp (×wμ−pol ) × wppfx ,

(5.7)

where wμ−pol is only applied for polarised muon decays. This total weight can be applied to all decays stored in the output files of the NuMI beamline simulation to build a flux histogram in a variable of interest, usually neutrino energy or angle.

5.6 NuMI Flux at MicroBooNE

63

5.6 NuMI Flux at MicroBooNE MicroBooNE is off-axis with respect to NuMI—offset both vertically and horizontally, as shown in Fig. 5.9. In addition, the NuMI decay pipe extends beyond MicroBooNE’s location. The resulting flux of neutrinos varies from an angle relative to the beamline direction of 8◦ from the NuMI target to backwards going neutrinos of 120◦ originating from the absorber.

5.6.1 Central Value Flux Prediction Neutrino direction and energy are correlated. Figure 5.10 shows the NuMI flux predictions for both FHC and RHC modes at MicroBooNE constrained with the PPFX package using the g4numi beam simulation. By being far off-axis, MicroBooNE sees a flux that originates mostly from unfocused mesons, resulting in relatively similar predictions for neutrinos and antineutrinos in both horn configurations. The single-bin peaks in the flux spectrum are due to two-body decays-at-rest from neutrino parents. The vast majority of neutrinos above 250 MeV of energy travel from the target direction, while the low energy neutrino (120◦ . There are also a number of sharp peaks in the flux at various angles. This is due to the production of neutrinos at different positions along the beamline e.g. at the absorber. Figure 5.12 shows the relationship between neutrino angle and the decay z position of the neutrino parents.

6

This calculation compares the neutrino travel time from the target to MicroBooNE with the sum of the neutrino travel time from the absorber to MicroBooNE and a 120 GeV proton’s time of flight from the target to the absorber.

5.6 NuMI Flux at MicroBooNE

ν / POT / 2 deg / cm2

FHC Mode ν µ (52.0%)

Target Absorber

−10

10

ν e (13.6%) ν µ (33.4%) ν e (1.0%)

−11

10

Decay Pipe

10−12

Muon Shield

10−13 10−14 10−150

20

40

60

80

100 120 140 Neutrino Angle [deg]

RHC Mode

ν / POT / 2 deg / cm2

Fig. 5.11 The PPFX constrained central value flux prediction for all neutrino flavours in the FHC and RHC modes in neutrino angle. No integration threshold is applied in the percentages and the electron neutrino flux percentage is boosted by muon decay at rest. The large angular spread in the flux is due to the positioning of MicroBooNE with respect to the NuMI beamline. The flux peaks at the target location and tails off further into the beamline. From angles above 20◦ , (midway into the decay pipe) the flux remains flat up-to-the absorber where there is a large peak in the flux spectrum ∼120◦ . After this, the flux is attenuated rapidly going into the muon-shield >120◦

65

Target Absorber

10−10

ν µ (43.8%) ν e (11.0%) ν µ (43.2%)

10−11

ν e (2.1%)

Decay Pipe

10−12

Muon Shield

−13

10

10−14 10−150

20

40

60

80

100 120 140 Neutrino Angle [deg]

5.6.2 Flux Prediction by Neutrino Parent The neutrino parents mostly include decays from pions, kaons and muons. Table 5.3, shows the channels available for these particles to decay into neutrinos with their respective branching ratios. Figure 5.13 shows the flux predictions broken down by parent type for each neutrino flavour in FHC mode. The muon neutrino flux is dominated by pion decay at energies below 1 GeV. For energies above 1 GeV, decays from kaons contribute almost entirely to the flux. This is similar for muon antineutrinos except that this switch over occurs around 2 GeV. In contrast, due to the small branching ratio of pion decays to electron neutrinos, the decays of pions to the electron neutrino flux is negligible. Decays from muons at rest (MuDAR) produce a significant electron neutrino and antineutrino flux, although, this is only up to ∼60 MeV where the cross section is vanishingly small. Muon decays in-flight contribute to a small fraction of the electron neutrino flux up to 250 MeV. The rest of the electron neutrino and antineutrino flux is almost entirely from kaon decays.

5 The NuMI Beam and Neutrino Flux Prediction at MicroBooNE Neutrino Angle [deg]

66

70000

120

60000 100 50000 80 40000 60 30000 40

20000

20

0 0

10000

100

200

300 400 500 600 700 800 Decay z Position in Beamline [m]

0

Fig. 5.12 A plot showing the relationship between neutrino angle and z decay position of the neutrino parents. The majority of neutrinos come from an angle close to the target location (z = 0 m). The NuMI absorber is located at 120◦ . The decay pipe starts around 50 m along the beamline. The colour scale shows the number of entries in each bin. This plot is made for electron neutrinos and antineutrinos that interact in MicroBooNE for a total of 2.4 × 1022 POT

The flux broken down by neutrino parent in FHC mode as a function of neutrino angle for each neutrino flavour is shown in Fig. 5.14. For the muon neutrino and antineutrino fluxes, the pion decays dominate the flux across all angles. In the case of ν¯ μ , there is a significant contribution from the decay of μ+ from the decay pipe onwards. For both electron neutrinos and antineutrinos, neutrinos from MuDAR populate the flux spectrum across all angles. Decays from kaons are most important near lower angles which correlates with the high energy kaon decays at the target location. However, there is also a significant kaon flux from the absorber location attributed to kaon decays at rest.

5.6.3 Flux Prediction in Energy and Angle To get the full perspective for the NuMI flux at MicroBooNE, the flux prediction is binned in energy and angle as shown in Fig. 5.15. The flux presents a strong energy and angle correlation. This is because neutrinos reaching MicroBooNE for larger angles are less probable to reach the detector as the energy of the neutrino parent

5.6 NuMI Flux at MicroBooNE

67

Table 5.3 The main decay channels from pions, kaons and muons that produce electron and muon neutrinos. Decay channel Branching ratio [%]

10−9 10−10 10−11

2

ν / POT / 25 MeV / cm

(Eν > 60 MeV)

Total Flux π+ (80.2%) π- (0.0%) μ+ (0.0%) μ- (3.6%) + K (15.7%) K (0.0%) 0 KL (0.5%)

10−8

10−8

10−11

10−13

10−13 1.5

2

2.5

νe

FHC Mode

(Eν > 60 MeV)

Total Flux π+ (0.9%) π- (0.0%) μ+ (13.3%) μ- (0.0%) + K (55.0%) K (0.0%) 0 KL (30.8%)

10−9 10−10 10−11

10−140

3 3.5 4 Energy [GeV]

0.5

1

1.5

2

2.5

νe

FHC Mode 2

10−8

1

(Eν > 60 MeV)

Total Flux π+ (0.0%) π- (88.7%) μ+ (0.5%) μ- (0.0%) + K (0.0%) K (9.9%) 0 KL (0.8%)

10−10

10−12

0.5

νμ

FHC Mode

10−9

10−12

10−140

ν / POT / 25 MeV / cm2

νμ

FHC Mode

99.9877 0.0123 63.55 5.07 3.353 40.6 27.04 100

ν / POT / 25 MeV / cm

ν / POT / 25 MeV / cm 2

π ± → μ± + νμ (¯νμ ) π ± → e± + νe (¯νe ) K ± → μ± + νμ K ± → νe (¯νe ) + e± + π 0 K ± → νμ (¯νμ ) + μ± + π 0 K L0 → νe (¯νe ) + e± + π ∓ K L0 → νμ (¯νμ ) + μ± + π ∓ μ± → e± + νe (¯νe ) + ν¯ μ (νμ )

3 3.5 4 Energy [GeV] (Eν > 60 MeV)

Total Flux π+ (0.0%) π- (0.5%) μ+ (0.0%) μ- (7.7%) + K (0.0%) K (35.2%) 0 KL (56.5%)

10−10 10−11 10−12

10−12 10−13

10−13 10−14

0

0.5

1

1.5

2

2.5

3 4 3.5 Energy [GeV]

10−14

0

0.5

1

1.5

2

2.5

3 4 3.5 Energy [GeV]

Fig. 5.13 The constrained FHC central value neutrino flux broken down by parent for each neutrino flavour. A 60 MeV threshold has been included in the percentages shown to avoid the flux from muon decay dominating these numbers

increases (because they are more forward boosted). For energies above 1.5 GeV, the entire composition of the flux originates from the target location. Conversely, neutrinos originating from angles >120◦ are possible only for energies below 250 MeV.

68

5 The NuMI Beam and Neutrino Flux Prediction at MicroBooNE

νμ

10−10 10−11 10−12

2

10−11

10−12

40

60

80

100

120

140

160

10−14

180

20

40

60

80

100

120

Angle [deg]

νe

2

ν / POT / 2 deg / cm

10−12

160

180

νe

FHC Mode

Total Flux π+ (0.0%) π- (0.0%) μ+ (95.4%) μ- (0.0%) + K (2.9%) K (0.0%) 0 KL (1.6%)

10−11

140

Angle [deg] 2

20

FHC Mode

ν / POT / 2 deg / cm

Total Flux π+ (0.0%) π- (55.3%) μ+ (38.8%) μ- (0.0%) + K (0.0%) K (5.5%) 0 KL (0.5%)

10−10

10−13

10−13 10−14

νμ

FHC Mode

Total Flux π+ (86.0%) π- (0.0%) μ+ (0.0%) μ- (3.9%) + K (9.9%) K (0.0%) 0 KL (0.3%)

ν / POT / 2 deg / cm

ν / POT / 2 deg / cm

2

FHC Mode

Total Flux π+ (0.0%) π- (0.2%) μ+ (0.0%) μ- (63.6%) + K (0.0%) K (13.5%) 0 KL (21.7%)

10−12

10−13 10−13

10−14

20

40

60

80

100

120

140

160

10−14

180

20

40

60

80

100

Angle [deg]

120

140

160

180

Angle [deg]

140

10−10

120 10−11

100 80

40

2

10−11

120

10−12

60 10−13

40

10−13

20 2.5

2

3 4 3.5 Energy [GeV]

10−14

νe

FHC Mode

140 10−11

120 100

10−12

80

160

0.5

1

1.5

2

2.5

3 4 3.5 Energy [GeV]

10−13

40

10−14

νe

FHC Mode

140

10−12

120 100 80 10−13

60

60

40 20

20 0 0

0 0

2

1.5

ν / POT / GeV / cm

1

Angle [deg]

0.5

ν / POT / GeV / cm2

0 0

Angle [deg]

140

80

20

160

νμ

FHC Mode

100

10−12

60

160

ν / POT / GeV / cm

νμ

FHC Mode

Angle [deg]

160

ν / POT / GeV / cm2

Angle [deg]

Fig. 5.14 The constrained FHC central value neutrino flux broken down by parent for each neutrino flavour. The percentages shown do not include an integration threshold on the angle. Decays from pions and muons dominate the majority of the flux across all angles

0.5

1

1.5

2

2.5

3 3.5 4 Energy [GeV]

10−14

0 0

0.5

1

1.5

2

2.5

3 3.5 4 Energy [GeV]

10−14

Fig. 5.15 The constrained FHC central value neutrino flux broken down in energy and angle for each neutrino flavour

5.7 Flux Uncertainties

69

5.7 Flux Uncertainties The uncertainties on the neutrino flux prediction are broken down into two main categories: uncertainties relating to the production of the neutrino parents following the collision of protons with a target (hadron production uncertainties) and uncertainties relating to the simulation and modelling of the NuMI beamline (beamline geometry uncertainties). This section describes how each of these systematic uncertainties are calculated and gives their estimated magnitude.

5.7.1 Hadron Production Uncertainties The uncertainties on the hadron production can be calculated using a multi-parameter resampling technique using PPFX. In this technique, all the parameters used within PPFX to constrain the flux prediction are sampled within their estimated uncertainties for each decay to a neutrino. This resampling, with each sample known as a “universe”, produces a weight which is applied on top of the total flux weight described in Sect. 5.5 to calculate an alternate flux prediction. These samples take into account the bin-to-bin correlations between each of these parameters. Figure 5.16 shows the FHC central value flux in black along with the mean of 600 weighted flux distributions in red. The standard deviation of each of the weighted distributions is shown by the grey uncertainty band. A wide, uneven binning is chosen to minimise statistical fluctuations per bin. Narrow bins are used to contain the mono-energetic decays-at-rest processes which can have large uncertainties. A covariance matrix, E i j , is evaluated using the central value and the Nuni multisims by the equation, Ei j =

Nuni 1  (x s − xicv )(x sj − x cv j ), Nuni s=0 i

(5.8)

where i, j are bin indexes and x is the quantity we want to study e.g. the flux prediction. This formalism assumes that the uncertainty is Gaussian; therefore, the systematic uncertainty in each bin is given by, σi =



E ii ,

(5.9)

which is equivalent to the standard deviation of all universes in each bin with respect to the CV. While the covariance matrix encodes information about the bin-to-bin correlations and uncertainty of a parameter, it is difficult to visually get this information from the matrix. It is useful to calculate a correlation matrix to visualise the bin-to-bin correlations,

70

5 The NuMI Beam and Neutrino Flux Prediction at MicroBooNE νμ νμ / POT / cm 2 / GeV

νμ / POT / cm 2 / GeV

νμ

FHC Mode

FHC Mode

10−7

Mean Flux

10−8

CV Flux

10−9 10−10 10−11

10−8

Mean Flux

10−9

CV Flux

10−10 10−11 10−12

10−12 10−13 0

10−13 1

2

3

4

5

7 8 9 10 6 Neutrino Energy [GeV]

0

1

2

3

4

νe Mean Flux 10−9

CV Flux

−10

10

−11

10

7 8 9 10 6 Neutrino Energy [GeV]

νe

FHC Mode

νe / POT / cm2 / GeV

νe / POT / cm2 / GeV

FHC Mode

5

Mean Flux

10−10

CV Flux

10−11

10−12 10−12 10−13

10−13 0

0.5

1

1.5

2

2.5

3 3.5 4 4.5 5 Neutrino Energy [GeV]

0

0.5

1

1.5

2

2.5

3 3.5 4 4.5 5 Neutrino Energy [GeV]

Fig. 5.16 The central value FHC flux in black along with the mean of 600 weighted flux distributions in red. The standard deviation of each of the weighted distributions is shown by the grey uncertainty band

ρi j = √

Ei j 

E ii

E jj

,

(5.10)

where −1 ≤ ρi j ≤ 1, and a fractional covariance matrix, Fi j , to visualise the fractional uncertainties: Ei j (5.11) Fi j = cv cv . xi x j The hadron production channels constrained by PPFX are summarised in Table 5.4. The fractional uncertainties for the NuMI flux in FHC mode are shown for each neutrino flavour in Fig. 5.17. The black line gives the total uncertainty, while the coloured lines show this uncertainty broken down by hadron production channel. It can be seen that for all neutrino flavours the Meson Incident, Nucleon-A and Nucleon X have the largest uncertainty. External data for these production modes is generally scarce and also contributes significantly to the uncertainty in the flux prediction in the similar energy range for MINERvA and NOvA [6]. The lowest energy bins ( 4.7